TY - CHAP A1 - Pokutta, Sebastian A1 - Schmaltz, Christian T1 - Optimal degree of centralization of liquidity management T2 - Proceedings of 22nd Australasian Finance and Banking Conference Y1 - 2009 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1458963 ER - TY - CHAP A1 - Lan, G. A1 - Pokutta, Sebastian A1 - Zhou, Y. A1 - Zink, Daniel T1 - Conditional Accelerated Lazy Stochastic Gradient Descent T2 - Proceedings of the International Conference on Machine Learning (ICML) Y1 - 2017 N1 - URL of the PDF: http://proceedings.mlr.press/v70/lan17a.html N1 - URL of the Poster: https://app.box.com/s/wnwym0p3eby54abb5bidnz7gznlkentq ER - TY - CHAP A1 - Inanlouganji, A. A1 - Pedrielli, G. A1 - Fainekos, G. A1 - Pokutta, Sebastian T1 - Continuous Simulation Optimization with Model Mismatch Using Gaussian Process Regression T2 - Proceedings of the 2018 Winter Simulation Conference Y1 - 2018 ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Singh, M. A1 - Torrico, A. T1 - Efficient algorithms for robust submodular maximization under matroid constraints T2 - ICML Workshop Paper Y1 - 2018 N1 - Additional Note: https://arxiv.org/abs/1807.09405 N1 - URL of the PDF: https://sites.google.com/view/icml2018nonconvex/papers ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Tu, Dan A1 - Wright, Stephen T1 - Blended Conditional Gradients: the unconditioning of conditional gradients T2 - Proceedings of ICML Y1 - 2019 N1 - Additional Note: https://arxiv.org/abs/1805.07311 N1 - URL of the Code: https://github.com/pokutta/bcg N1 - URL of the PDF: http://proceedings.mlr.press/v97/braun19a/braun19a.pdf N1 - URL of the Poster: https://app.box.com/s/nmmm671jd72i397nysa8emfnzh1hn6hf N1 - URL of the Slides: https://app.box.com/s/xbx3z7ws6dxvl3rzgj4jp6forigycooe N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2019/02/18/bcg-abstract.html ER - TY - CHAP A1 - Diakonikolas, Jelena A1 - Carderera, Alejandro A1 - Pokutta, Sebastian T1 - Breaking the Curse of Dimensionality (Locally) to Accelerate Conditional Gradients T2 - OPTML Workshop Paper Y1 - 2019 N1 - URL of the Code: https://colab.research.google.com/drive/1ejjfCan7xnEhWWJXCIzb03CwQRG9iW_O N1 - URL of the PDF: https://opt-ml.org/papers/2019/paper_26.pdf N1 - URL of the Poster: https://app.box.com/s/d7p038u7df422q4jsccbmj15mngqv2ws N1 - URL of the Slides: https://app.box.com/s/gphkhapso7d1vrfnzqykkb3vx0agxh8w N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2019/07/04/LaCG-abstract.html ER - TY - CHAP A1 - Combettes, Cyrille W. A1 - Pokutta, Sebastian T1 - Blended Matching Pursuit T2 - Proceedings of NeurIPS Y1 - 2019 N1 - URL of the Code: https://colab.research.google.com/drive/17XYIxnCcJjKswba9mAaXFWnNGVZdsaXQ N1 - URL of the PDF: https://papers.nips.cc/paper/8478-blended-matching-pursuit N1 - URL of the Poster: https://app.box.com/s/j6lbh49udjd45krhxcypufxwdofw6br8 N1 - URL of the Slides: https://app.box.com/s/8lfktq6h3dqp9t2gqydu2tp8h2uxgz7m N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2019/05/27/bmp-abstract.html ER - TY - CHAP A1 - Kerdreux, T. A1 - d’Aspremont, A. A1 - Pokutta, Sebastian T1 - Restarting Frank-Wolfe T2 - Proceedings of AISTATS Y1 - 2019 N1 - URL of the PDF: http://proceedings.mlr.press/v89/kerdreux19a/kerdreux19a.pdf N1 - URL of the Slides: https://app.box.com/s/prd32r6xmuef2k4gah23rd0egllz9rv5 N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2019/05/02/restartfw-abstract.html ER - TY - CHAP A1 - Anari, N. A1 - Haghtalab, N. A1 - Naor, S. A1 - Pokutta, Sebastian A1 - Singh, M. A1 - Torrico, A. T1 - Structured Robust Submodular Maximization: Offline and Online Algorithms T2 - Proceedings of AISTATS Y1 - 2019 N1 - URL of the PDF: http://proceedings.mlr.press/v89/anari19a/anari19a.pdf ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Singh, M. A1 - Torrico, A. T1 - On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts to Sharpness T2 - OPTML Workshop Paper Y1 - 2019 N1 - URL of the PDF: https://opt-ml.org/papers/2019/paper_16.pdf N1 - URL of the Poster: https://app.box.com/s/24vbh1s2vib11upqyepzen3lzdl13skr ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Strüngmann, L. T1 - The Chase radical and reduced products JF - Journal of Pure and Applied Algebra Y1 - 2007 N1 - Additional Note: doi:10.1016/j.jpaa.2007.02.007 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.jpaa.2007.02.007 VL - 211 SP - 532 EP - 540 ER - TY - JOUR A1 - Droste, M. A1 - Göbel, R. A1 - Pokutta, Sebastian T1 - Absolute graphs with prescribed endomorphism monoid JF - Semigroup Forum Y1 - 2008 N1 - URL of the PDF: http://dx.doi.org/doi:10.1007/s00233-007-9029-1 VL - 76 SP - 256 EP - 267 ER - TY - JOUR A1 - Göbel, R. A1 - Pokutta, Sebastian T1 - Construction of dual modules using Martin’s axiom JF - Journal of Algebra Y1 - 2008 N1 - Additional Note: doi:10.1016/j.jalgebra.2008.06.017 N1 - URL of the PDF: https://www.sciencedirect.com/science/article/pii/S0021869308003153 VL - 320 SP - 2388 EP - 2404 ER - TY - JOUR A1 - Heldt, D. A1 - Kreuzer, M. A1 - Pokutta, Sebastian A1 - Poulisse, H. T1 - Approximate Computation of zero-dimensional polynomial ideals JF - Journal of Symbolic Computation Y1 - 2009 N1 - Additional Note: doi:10.1016/j.jsc.2008.11.010 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.jsc.2008.11.010 VL - 44 SP - 1566 EP - 1591 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Stauffer, G. T1 - France Telecom Workforce Scheduling Problem: a challenge JF - RAIRO-Operations Research Y1 - 2009 N1 - Additional Note: DOI: 10.1051/ro/2009025 N1 - URL of the PDF: http://dx.doi.org/10.1051/ro/2009025 IS - 43 SP - 375 EP - 386 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - Random half-integral polytopes JF - Operations Research Letters Y1 - 2011 UR - http://www.optimization-online.org/DB_HTML/2010/11/2813.html N1 - Additional Note: doi:10.1016/j.orl.2011.03.003 VL - 39 IS - 3 SP - 204 EP - 207 ER - TY - JOUR A1 - Haus, Utz-Uwe A1 - Hemmecke, R. A1 - Pokutta, Sebastian T1 - Reconstructing biochemical cluster networks JF - Journal of Mathematical Chemistry Y1 - 2011 N1 - URL of the PDF: http://dx.doi.org/10.1007/s10910-011-9892-6 VL - 49 IS - 10 SP - 2441 EP - 2456 ER - TY - JOUR A1 - Letchford, A.N. A1 - Pokutta, Sebastian A1 - Schulz, A.S. T1 - On the membership problem for the 0,1/2-closure JF - Operations Research Letters Y1 - 2011 UR - http://www.box.net/shared/zxx88q38l3 N1 - Additional Note: doi:10.1016/j.orl.2011.07.003 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.orl.2011.07.003 VL - 39 IS - 5 SP - 301 EP - 304 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Schulz, A.S. T1 - Integer-empty polytopes in the 0/1-cube with maximal Gomory-Chvátal rank JF - Operations Research Letters Y1 - 2011 UR - http://www.optimization-online.org/DB_HTML/2010/12/2850.html N1 - Additional Note: doi:10.1016/j.orl.2011.09.004 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.orl.2011.09.004 VL - 39 IS - 6 SP - 457 EP - 460 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Schmaltz, Christian T1 - Managing liquidity: Optimal degree of centralization JF - Journal of Banking and Finance KW - Real options Y1 - 2011 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1458963 U6 - https://doi.org/DOI: 10.1016/j.jbankfin.2010.07.001 SN - 0378-4266 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.jbankfin.2010.07.001 VL - 35 SP - 627 EP - 638 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Stauffer, G. T1 - Lower bounds for the Chvátal-Gomory rank in the 0/1 cube JF - Operations Research Letters Y1 - 2011 UR - http://www.optimization-online.org/DB_HTML/2010/09/2748.html N1 - Additional Note: doi:10.1016/j.orl.2011.03.001 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.orl.2011.03.001 VL - 39 IS - 3 SP - 200-203 ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - Rank of random half-integral polytopes T2 - Electronic Notes in Discrete Mathematics Y1 - 2010 UR - http://www.box.net/shared/0zx04174bg N1 - Additional Note: doi:10.1016/j.endm.2010.05.053 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.endm.2010.05.053 VL - 36 SP - 415 EP - 422 ER - TY - CHAP A1 - Drewes, S. A1 - Pokutta, Sebastian T1 - Cutting-planes for weakly-coupled 0/1 second order cone programs T2 - Electronic Notes in Discrete Mathematics Y1 - 2010 UR - http://www.box.net/shared/4k2qtsl65k N1 - Additional Note: doi:10.1016/j.endm.2010.05.093 N1 - URL of the PDF: http://dx.doi.org/j.endm.2010.05.093 VL - 36 SP - 735 EP - 742 ER - TY - CHAP A1 - Drewes, S. A1 - Pokutta, Sebastian T1 - Geometric mean maximization in the presence of discrete decisions T2 - Proceedings of 23rd Australasian Finance and Banking Conference Y1 - 2010 ER - TY - CHAP A1 - Martin, Alexander A1 - Müller, J. A1 - Pokutta, Sebastian T1 - On clearing coupled day-ahead electricity markets T2 - Proceedings of 23rd Australasian Finance and Banking Conference Y1 - 2010 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1660528 N1 - Additional Note: doi:10.1080/10556788.2013.823544 ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Schulz, A.S. T1 - On the rank of generic cutting-plane proof systems T2 - Proceedings of IPCO, Lecture Notes in Computer Science Y1 - 2010 UR - http://www.optimization-online.org/DB_HTML/2013/02/3782.html N1 - Additional Note: doi:10.1007/978-3-642-13036-6_34 N1 - URL of the PDF: http://dx.doi.org/10.1007/978-3-642-13036-6_34 VL - 6080 SP - 450 EP - 463 ER - TY - CHAP A1 - Helmke, H. A1 - Gluchshenko, O. A1 - Martin, Alexander A1 - Peter, A. A1 - Pokutta, Sebastian A1 - Siebert, U. T1 - Optimal Mixed-Mode Runway Scheduling T2 - Proceedings of DACS Y1 - 2011 UR - http://www.box.net/shared/34p1ea2of7exdgq7tlty ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Schmaltz, Christian T1 - A network model for bank lending capacity T2 - Proceedings of Systemic Risk, Basel III, Financial Stability and Regulation Y1 - 2011 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773964 ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Schmaltz, Christian T1 - Optimal Planning under Basel III Regulations T2 - Proceedings of 24th Australasian Finance and Banking Conference Y1 - 2011 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1914800 ER - TY - CHAP A1 - Braun, Gábor A1 - Fiorini, Samuel A1 - Pokutta, Sebastian A1 - Steurer, D. T1 - Approximation Limits of Linear Programs (Beyond Hierarchies) T2 - Proceedings of FOCS Y1 - 2012 ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - An algebraic view on symmetric extended formulations T2 - Proceedings of ISCO, Lecture Notes in Computer Science Y1 - 2012 VL - 7422 IS - 141--152 ER - TY - CHAP A1 - Fiorini, Samuel A1 - Massar, S. A1 - Pokutta, Sebastian A1 - Tiwary, H.R. A1 - de Wolf, R. T1 - Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds T2 - Proceedings of STOC Y1 - 2012 ER - TY - CHAP A1 - Schmaltz, Christian A1 - Pokutta, Sebastian A1 - Heidorn, Thomas A1 - Andrae, Silvio T1 - How to make regulators and shareholders happy under Basel III T2 - Proceedings of the 26th Australasian Finance and Banking Conference Y1 - 2013 UR - http://ssrn.com/abstract=2179490 N1 - Additional Note: 10.1016/j.jbankfin.2014.05.031 ER - TY - CHAP A1 - Briët, Jop A1 - Dadush, Daniel A1 - Pokutta, Sebastian T1 - On the existence of 0/1 polytopes with high semidefinite extension complexity T2 - Proceedings of ESA Y1 - 2013 ER - TY - CHAP A1 - Braun, Gabor A1 - Pokutta, Sebastian T1 - Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium T2 - Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium Y1 - 2013 UR - http://eccc.hpi-web.de/report/2013/056 SP - 688 EP - 697 ER - TY - CHAP A1 - Braun, Gábor A1 - Fiorini, Samuel A1 - Pokutta, Sebastian T1 - Average case polyhedral complexity of the maximum stable set problem T2 - Proceedings of RANDOM Y1 - 2014 N1 - Additional Note: http://www.dagstuhl.de/dagpub/978-3-939897-74-3 N1 - URL of the PDF: http://www.dagstuhl.de/dagpub/978-3-939897-74-3 ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Xie, Y. T1 - Info-Greedy Sequential Adaptive Compressed Sensing T2 - Proceedings of 52nd Annual Allerton Conference on Communication, Control, and Computing Y1 - 2014 ER - TY - CHAP A1 - Bazzi, Abbas A1 - Fiorini, Samuel A1 - Pokutta, Sebastian A1 - Svensson, Ola T1 - Small linear programs cannot approximate Vertex Cover within a factor of 2 - epsilon T2 - Proceedings of FOCS Y1 - 2015 N1 - URL of the Slides: https://app.box.com/s/00aqupo722bbpmdcyzwt8xmfqzyu14iy ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - The matching polytope does not admit fully-polynomial size relaxation schemes T2 - Proceeedings of SODA Y1 - 2015 ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Zink, Daniel T1 - Inapproximability of combinatorial problems via small LPs and SDPs T2 - Proceeedings of STOC Y1 - 2015 ER - TY - CHAP A1 - Pokutta, Sebastian T1 - Information Theory and Polyhedral Combinatorics T2 - Proceedings of 53rd Annual Allerton Conference on Communication, Control, and Computing Y1 - 2015 N1 - Additional Note: http://ieeexplore.ieee.org/abstract/document/7447134/ N1 - URL of the PDF: http://ieeexplore.ieee.org/abstract/document/7447134/ ER - TY - CHAP A1 - Song, R. A1 - Xie, Y. A1 - Pokutta, Sebastian T1 - Sequential Sensing with Model Mismatch T2 - Proceedings of ISIT Y1 - 2015 ER - TY - CHAP A1 - Xie, Y. A1 - Li, Q. A1 - Pokutta, Sebastian T1 - Supervised Online Subspace Tracking T2 - Proceedings of Asilomar Conference on Signals, Systems, and Computers Y1 - 2015 ER - TY - CHAP A1 - Roy, Aurko A1 - Pokutta, Sebastian T1 - Hierarchical Clustering via Spreading Metrics T2 - Proceedings of NIPS Y1 - 2016 N1 - Additional Note: http://https://papers.nips.cc/paper/by-source-2016-1199 https://arxiv.org/abs/1610.09269 N1 - URL of the PDF: https://papers.nips.cc/paper/by-source-2016-1199 ER - TY - CHAP A1 - Braun, Gábor A1 - Roy, Aurko A1 - Pokutta, Sebastian T1 - Stronger Reductions for Extended Formulations T2 - Proceedings of IPCO Y1 - 2016 ER - TY - CHAP A1 - Braun, Gábor A1 - Brown-Cohen, Jonah A1 - Huq, Arefin A1 - Pokutta, Sebastian A1 - Raghavendra, Prasad A1 - Weitz, Benjamin A1 - Zink, Daniel T1 - The matching problem has no small symmetric SDP T2 - Proceddings of SODA 2016 Y1 - 2016 N1 - URL of the PDF: http://ieeexplore.ieee.org/abstract/document/7447134/ ER - TY - CHAP A1 - Roy, Aurko A1 - Xu, Huan A1 - Pokutta, Sebastian T1 - Reinforcement Learning under Model Mismatch T2 - Proceedings of NIPS Y1 - 2017 N1 - Additional Note: http://https://papers.nips.cc/paper/by-source-2016-1199 https://arxiv.org/abs/1610.09269 ER - TY - CHAP A1 - Bärmann, Andreas A1 - Pokutta, Sebastian A1 - Schneider, Oskar T1 - Emulating the Expert: Inverse Optimization through Online Learning T2 - Proceedings of the International Conference on Machine Learning (ICML) Y1 - 2017 N1 - URL of the PDF: http://proceedings.mlr.press/v70/barmann17a.html N1 - URL of the Poster: https://app.box.com/s/h3ychkv99il7oyzw7sym8la5lhit3elg N1 - URL of the Slides: https://app.box.com/s/7ti8sz8mf5s2znn1qo32in4jxy5gjnn1 N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2018/11/25/expertLearning-abstract.html ER - TY - CHAP A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Zink, Daniel T1 - Lazifying Conditional Gradient Algorithms T2 - Proceedings of the International Conference on Machine Learning (ICML) Y1 - 2017 N1 - URL of the PDF: http://proceedings.mlr.press/v70/braun17a N1 - URL of the Poster: https://app.box.com/s/lysscdg17ytpz7mqr0tu2djffyqvkl6a N1 - URL of the Slides: https://app.box.com/s/zsp0hixjz2ha23u1vuyosijjkjdh8kj7 ER - TY - CHAP A1 - Arumugam, Keerthi Suria Kumar A1 - Kadampot, Ishaque Ashar A1 - Tahmasbi, Mehrdad A1 - Shah, Shaswat A1 - Bloch, Matthieu A1 - Pokutta, Sebastian T1 - Modulation Recognition Using Side Information and Hybrid Learning T2 - Proceedings of IEEE DySPAN Y1 - 2017 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Zimmer, Max T1 - Deep Neural Network Training with Frank-Wolfe N2 - This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw comparisons both to current state-of-the-art stochastic Gradient Descent methods as well as across different variants of stochastic Conditional Gradients. In particular, we show the general feasibility of training Neural Networks whose parameters are constrained by a convex feasible region using Frank-Wolfe algorithms and compare different stochastic variants. We then show that, by choosing an appropriate region, one can achieve performance exceeding that of unconstrained stochastic Gradient Descent and matching state-of-the-art results relying on L2-regularization. Lastly, we also demonstrate that, besides impacting performance, the particular choice of constraints can have a drastic impact on the learned representations. Y1 - 2020 ER - TY - JOUR A1 - Cryille W., Combettes A1 - Spiegel, Christoph A1 - Pokutta, Sebastian T1 - Projection-Free Adaptive Gradients for Large-Scale Optimization N2 - The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational burdens, by querying only approximate first-order information from the objective and by maintaining feasibility of the iterates without using projections. In this paper, we improve the quality of their first-order information by blending in adaptive gradients. We derive convergence rates and demonstrate the computational advantage of our method over the state-of-the-art stochastic Frank-Wolfe algorithms on both convex and nonconvex objectives. The experiments further show that our method can improve the performance of adaptive gradient algorithms for constrained optimization. Y1 - 2020 ER - TY - CHAP A1 - Pfetsch, Marc A1 - Pokutta, Sebastian T1 - IPBoost – Non-Convex Boosting via Integer Programming T2 - Proceedings of ICML Y1 - 2020 N1 - URL of the Code: https://www2.mathematik.tu-darmstadt.de/~pfetsch/ipboost.html N1 - URL of the Slides: https://app.box.com/s/8dpvmls88suouy11bkpwufhu7iiz6dxl N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/02/13/ipboost-abstract.html ER - TY - CHAP A1 - Pokutta, Sebastian A1 - Singh, M. A1 - Torrico, A. T1 - On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts to Sharpness T2 - Proceedings of ICML Y1 - 2020 N1 - URL of the Poster: https://app.box.com/s/24vbh1s2vib11upqyepzen3lzdl13skr N1 - URL of the Slides: https://app.box.com/s/fmjxhfdpiqubm28upf563ohy8t8fgl3a N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/06/03/unreasonable-abstract.html N1 - https://www.youtube.com/watch?v=VB1e0HrDmVo ER - TY - CHAP A1 - Diakonikolas, Jelena A1 - Carderera, Alejandro A1 - Pokutta, Sebastian T1 - Locally Accelerated Conditional Gradients T2 - Proceedings of AISTATS Y1 - 2020 N1 - URL of the Code: https://colab.research.google.com/drive/1ejjfCan7xnEhWWJXCIzb03CwQRG9iW_O N1 - URL of the PDF: http://proceedings.mlr.press/v108/diakonikolas20a/diakonikolas20a.pdf N1 - URL of the Slides: https://app.box.com/s/gphkhapso7d1vrfnzqykkb3vx0agxh8w N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2019/07/04/LaCG-abstract.html N1 - https://slideslive.com/38930107/locally-accelerated-conditional-gradients?ref=account-folder-52123-folders ER - TY - JOUR A1 - Anari, N. A1 - Haghtalab, N. A1 - Naor, S. A1 - Pokutta, Sebastian A1 - Singh, M. A1 - Torrico, A. T1 - Structured Robust Submodular Maximization: Offline and Online Algorithms JF - INFORMS Journal on Computing Y1 - 2020 ER - TY - CHAP A1 - Combettes, Cyrille W. A1 - Pokutta, Sebastian T1 - Boosting Frank-Wolfe by Chasing Gradients T2 - Proceedings of ICML Y1 - 2020 N1 - Additional Note: github code: https://github.com/cyrillewcombettes/boostfw N1 - URL of the Code: https://colab.research.google.com/drive/1TSOVjDFF1X2ADBo_adHLsUVrblSutRKw N1 - URL of the Slides: https://app.box.com/s/wwj247r5d456q0778p9b9y1jm6txuifb N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/03/16/boostFW.html N1 - https://www.youtube.com/watch?v=BfyV0C5FRbE ER - TY - CHAP A1 - Mortagy, Hassan A1 - Gupta, Swati A1 - Pokutta, Sebastian T1 - Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization T2 - Proceedings of NeurIPS Y1 - 2020 N1 - URL of the Code: https://github.com/pokutta/Walking-in-the-Shadow N1 - URL of the Poster: https://app.box.com/s/y266djezdjdidsswaopvdcnsnkp8774i N1 - URL of the Slides: https://app.box.com/s/wjhpe4nh8kv5pw6vl5jbp902v3mksivs ER - TY - CHAP A1 - Pokutta, Sebastian T1 - Restarting Algorithms: Sometimes there is Free Lunch T2 - Proceedings of CPAIOR Y1 - 2020 N1 - URL of the Slides: https://app.box.com/s/8ps8bhjv2phhy182xn55iurk9t3o1xc3 N1 - https://www.youtube.com/watch?v=v3Xzoda2_gQ ER - TY - JOUR A1 - Le Bodic, P. A1 - Pfetsch, Marc A1 - Pavelka, J. A1 - Pokutta, Sebastian T1 - Solving MIPs via Scaling-based Augmentation JF - Discrete Optimization Y1 - 2018 N1 - Additional Note: doi: 10.1016/j.disopt.2017.08.004 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.disopt.2017.08.004 VL - 27 SP - 1 EP - 25 ER - TY - JOUR A1 - Braun, Gábor A1 - Roy, Aurko A1 - Pokutta, Sebastian T1 - Stronger Reductions for Extended Formulations JF - to appear in Mathematical Programming B Y1 - 2018 N1 - Additional Note: available at \url{http://arxiv.org/abs/1512.04932} ER - TY - JOUR A1 - Song, R. A1 - Xie, Y. A1 - Pokutta, Sebastian T1 - On the effect of model mismatch for sequential Info-Greedy Sensing JF - EURASIP Journal on Advances in Signal Processing Y1 - 2018 N1 - URL of the PDF: https://asp-eurasipjournals.springeropen.com/articles/10.1186/s13634-018-0551-y ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Zink, Daniel T1 - Affine Reductions for LPs and SDPs JF - Mathematical Programming A Y1 - 2019 N1 - URL of the PDF: http://rdcu.be/EPf9 VL - 173 IS - 1 SP - 281 EP - 312 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Zink, Daniel T1 - Lazifying Conditional Gradient Algorithms JF - Journal of Machine Learning Research (JMLR) Y1 - 2019 N1 - URL of the PDF: http://jmlr.org/papers/v20/18-114.html N1 - URL of the Slides: https://app.box.com/s/zsp0hixjz2ha23u1vuyosijjkjdh8kj7 VL - 20 IS - 71 SP - 1 EP - 42 ER - TY - JOUR A1 - Bärmann, Andreas A1 - Heidt, Andreas A1 - Martin, Alex A1 - er, A1 - Pokutta, Sebastian A1 - Thurner, Christoph T1 - Polyhedral Approximation of Ellipsoidal Uncertainty Sets via Extended Formulations - a computational case study JF - Computational Management Science Y1 - 2016 UR - http://www.optimization-online.org/DB_HTML/2014/02/4245.html N1 - Additional Note: http://link.springer.com/article/10.1007/s10287-015-0243-0 DOI:10.1007/s10287-015-0243-0 N1 - URL of the PDF: http://link.springer.com/article/10.1007/s10287-015-0243-0 VL - 13 IS - 2 SP - 151 EP - 193 ER - TY - JOUR A1 - Roy, Aurko A1 - Pokutta, Sebastian T1 - Hierarchical Clustering via Spreading Metrics JF - Journal of Machine Learning Research (JMLR) Y1 - 2017 N1 - Additional Note: http://https://papers.nips.cc/paper/by-source-2016-1199 N1 - URL of the PDF: http://jmlr.org/papers/v18/17-081.html VL - 18 SP - 1 EP - 35 ER - TY - JOUR A1 - Bodur, Merve A1 - Del Pia, Alberto A1 - Dey, Santanu Sabush A1 - Molinaro, Marco A1 - Pokutta, Sebastian T1 - Aggregation-based cutting-planes for packing and covering Integer Programs JF - to appear in Mathematical Programming A Y1 - 2017 N1 - Additional Note: doi:10.1007/s10107-017-1192-x N1 - URL of the PDF: http://dx.doi.org/10.1007/s10107-017-1192-x ER - TY - JOUR A1 - Bazzi, Abbas A1 - Fiorini, Samuel A1 - Pokutta, Sebastian A1 - Svensson, Ola T1 - Small linear programs cannot approximate Vertex Cover within a factor of 2 - epsilon JF - to appear in Mathematics of Operations Research Y1 - 2017 N1 - URL of the Slides: https://app.box.com/s/00aqupo722bbpmdcyzwt8xmfqzyu14iy ER - TY - JOUR A1 - Braun, Gábor A1 - Guzmán, C. A1 - Pokutta, Sebastian T1 - Unifying Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization JF - IEEE Transactions of Information Theory Y1 - 2017 N1 - Additional Note: doi:10.1109/TIT.2017.2701343 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7919238 N1 - URL of the PDF: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7919238 VL - 63 IS - 7 SP - 4709 EP - 4724 ER - TY - JOUR A1 - Braun, Gábor A1 - Jain, R. A1 - Lee, T. A1 - Pokutta, Sebastian T1 - Information-theoretic approximations of the nonnegative rank JF - Computational Complexity Y1 - 2017 UR - http://eccc.hpi-web.de/report/2013/158 VL - 26 IS - 1 SP - 147 EP - 197 ER - TY - JOUR A1 - Christensen, H. A1 - Khan, A. A1 - Pokutta, Sebastian A1 - Tetali, P. T1 - Multidimensional Bin Packing and Other Related Problems: A survey JF - to appear in Computer Science Review Y1 - 2017 N1 - Additional Note: http://www.sciencedirect.com/science/article/pii/S1574013716301356 http://www.sciencedirect.com/science/article/pii/S1574013716301356 N1 - URL of the PDF: http://www.sciencedirect.com/science/article/pii/S1574013716301356 ER - TY - JOUR A1 - Martin, Alex A1 - Müller, J. A1 - Pape, S. A1 - Peter, A. A1 - Pokutta, Sebastian A1 - Winter, T. T1 - Pricing and clearing combinatorial markets with singleton and swap orders JF - Mathematical Methods of Operations Research Y1 - 2017 VL - 85 IS - 2 SP - 155 EP - 177 ER - TY - JOUR A1 - Knueven, B. A1 - Ostrowski, J. A1 - Pokutta, Sebastian T1 - Detecting Almost Symmetries in Graphs JF - to appear in Mathematical Programming C Y1 - 2017 UR - http://www.optimization-online.org/DB_HTML/2015/09/5117.html N1 - URL of the PDF: http://link.springer.com/article/10.1007/s12532-017-0124-3 ER - TY - JOUR A1 - Braun, Gábor A1 - Brown-Cohen, Jonah A1 - Huq, Arefin A1 - Pokutta, Sebastian A1 - Raghavendra, Prasad A1 - Weitz, Benjamin A1 - Zink, Daniel T1 - The matching problem has no small symmetric SDP JF - Mathematical Programming A Y1 - 2017 N1 - Additional Note: DOI 10.1007/s10107-016-1098-z N1 - URL of the PDF: http://dx.doi.org/10.1007/s10107-016-1098-z VL - 165 IS - 2 SP - 643 EP - 662 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - Rigid abelian groups and the probabilistic method JF - Contemporary Mathematics Y1 - 2012 N1 - Additional Note: doi:/10.1090/conm/576 N1 - URL of the PDF: http://dx.doi.org/10.1090/conm/576 VL - 576 SP - 17 EP - 30 ER - TY - JOUR A1 - Göbel, R. A1 - Pokutta, Sebastian T1 - Absolutely rigid fields and Shelah’s absolutely rigid trees JF - Contemporary Mathematics Y1 - 2012 UR - http://www.box.net/shared/numjyo0qxmpsz9dposyt N1 - Additional Note: doi:/10.1090/conm/576 N1 - URL of the PDF: http://dx.doi.org/10.1090/conm/576 VL - 576 SP - 105 EP - 128 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - Schmaltz, Christian T1 - Optimal Planning under Basel III Regulations JF - Cass-Capco Institute Paper Series on Risk Y1 - 2012 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1914800 N1 - Additional Note: http://www.capco.com/capco-institute/capco-journal/journal-34-cass-capco-institute-paper-series-on-risk N1 - URL of the PDF: http://www.capco.com/capco-institute/capco-journal/journal-34-cass-capco-institute-paper-series-on-risk VL - 34 ER - TY - JOUR A1 - Kroll, C. A1 - Pokutta, Sebastian T1 - Just a perfect day: developing a happiness optimised day schedule JF - Journal of Economic Psychology Y1 - 2013 N1 - Additional Note: doi:/10.1016/j.joep.2012.09.015 N1 - URL of the PDF: http://www.sciencedirect.com/science/article/pii/S0167487012001158 VL - 34 SP - 210 EP - 217 ER - TY - JOUR A1 - Pokutta, Sebastian A1 - VanVyve, M. T1 - A note on the extension complexity of the knapsack polytope JF - Operations Research Letters Y1 - 2013 UR - http://www.optimization-online.org/DB_HTML/2013/02/3787.html N1 - Additional Note: DOI information: 10.1016/j.orl.2013.03.010 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.orl.2013.03.010 VL - 41 SP - 347 EP - 350 ER - TY - JOUR A1 - Schmaltz, Christian A1 - Pokutta, Sebastian A1 - Heidorn, Thomas A1 - Andrae, Silvio T1 - How to make regulators and shareholders happy under Basel III JF - Journal of Banking and Finance Y1 - 2014 UR - http://ssrn.com/abstract=2179490 N1 - Additional Note: 10.1016/j.jbankfin.2014.05.031 N1 - URL of the PDF: http://dx.doi.org/10.1016/j.jbankfin.2014.05.031 SP - 311 EP - 325 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - A short proof for the polyhedrality of the Chvátal-Gomory closure of a compact convex set JF - Operations Research Letters Y1 - 2014 N1 - Additional Note: 10.1016/j.orl.2014.05.004 VL - 42 SP - 307 EP - 310 ER - TY - JOUR A1 - Drewes, S. A1 - Pokutta, Sebastian T1 - Computing discrete expected utility maximizing portfolios JF - Journal of Investing Y1 - 2014 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1662729 VL - 23 IS - 4 SP - 121 EP - 132 ER - TY - JOUR A1 - Drewes, S. A1 - Pokutta, Sebastian T1 - Symmetry-exploiting cuts for a class of mixed-0/1 second order cone programs JF - Discrete Optimization Y1 - 2014 UR - http://www.optimization-online.org/DB_HTML/2010/06/2652.html N1 - Additional Note: doi:10.1016/j.disopt.2014.04.002 VL - 13 SP - 23 EP - 35 ER - TY - JOUR A1 - Martin, Alexander A1 - Müller, J. A1 - Pokutta, Sebastian T1 - Strict linear prices in non-convex European day-ahead electricity markets JF - Optimization Methods and Software Y1 - 2014 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1660528 N1 - Additional Note: 10.1080/10556788.2013.823544 N1 - URL of the PDF: http://dx.doi.org/10.1080/10556788.2013.823544 VL - 29 IS - 1 SP - 189 EP - 221 ER - TY - JOUR A1 - Briët, Jop A1 - Dadush, Daniel A1 - Pokutta, Sebastian T1 - On the existence of 0/1 polytopes with high semidefinite extension complexity JF - Mathematical Programming B Y1 - 2015 VL - 153 IS - 1 SP - 179 EP - 199 ER - TY - JOUR A1 - Braun, Gábor A1 - Fiorini, Samuel A1 - Pokutta, Sebastian A1 - Steurer, D. T1 - Approximation Limits of Linear Programs (Beyond Hierarchies) JF - Mathematics of Operations Research Y1 - 2015 VL - 40 IS - 3 SP - 179 EP - 199 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - The matching polytope does not admit fully-polynomial size relaxation schemes JF - IEEE Transactions on Information Theory Y1 - 2015 N1 - Additional Note: doi:10.1109/TIT.2015.2465864 N1 - URL of the PDF: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7182355 VL - 61 IS - 10 SP - 1 EP - 11 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian A1 - Xie, Y. T1 - Info-Greedy Sequential Adaptive Compressed Sensing JF - IEEE Journal of Selected Topics in Signal Processing Y1 - 2015 VL - 9 IS - 4 SP - 601 EP - 611 ER - TY - JOUR A1 - Fiorini, Samuel A1 - Massar, S. A1 - Pokutta, Sebastian A1 - Tiwary, H.R. A1 - de Wolf, R. T1 - Exponential Lower Bounds for Polytopes in Combinatorial Optimization JF - Journal of the ACM Y1 - 2015 N1 - URL of the PDF: https://doi.org/10.1145/2716307 VL - 62 IS - 2 SP - 1 EP - 17 ER - TY - JOUR A1 - Braun, Gábor A1 - Fiorini, Samuel A1 - Pokutta, Sebastian T1 - Average case polyhedral complexity of the maximum stable set problem JF - Mathematical Programming A Y1 - 2016 N1 - Additional Note: http://www.dagstuhl.de/dagpub/978-3-939897-74-3 N1 - URL of the PDF: https://rdcu.be/7uOy VL - 160 IS - 1 SP - 407 EP - 431 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - A polyhedral characterization of Border Bases JF - SIAM Journal on Discrete Mathematics Y1 - 2016 VL - 30 IS - 1 SP - 239 EP - 265 ER - TY - JOUR A1 - Braun, Gábor A1 - Pokutta, Sebastian T1 - Common information and unique disjointness JF - Algorithmica Y1 - 2016 UR - http://eccc.hpi-web.de/report/2013/056 N1 - URL of the PDF: https://rdcu.be/6b9u VL - 76 IS - 3 SP - 597 EP - 629 ER - TY - JOUR A1 - Gatzert, Nadine A1 - Pokutta, Sebastian A1 - Vogl, Nikolai T1 - Convergence of Capital and Insurance Markets: Pricing Aspects of Index-Linked Catastrophic Loss Instruments JF - to appear in Journal of Risk and Insurance Y1 - 2016 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2320370 ER - TY - CHAP A1 - Carderera, Alejandro A1 - Diakonikolas, Jelena A1 - Lin, Cheuk Yin A1 - Pokutta, Sebastian T1 - Parameter-free Locally Accelerated Conditional Gradients T2 - ICML 2021 N2 - Projection-free conditional gradient (CG) methods are the algorithms of choice for constrained optimization setups in which projections are often computationally prohibitive but linear optimization over the constraint set remains computationally feasible. Unlike in projection-based methods, globally accelerated convergence rates are in general unattainable for CG. However, a very recent work on Locally accelerated CG (LaCG) has demonstrated that local acceleration for CG is possible for many settings of interest. The main downside of LaCG is that it requires knowledge of the smoothness and strong convexity parameters of the objective function. We remove this limitation by introducing a novel, Parameter-Free Locally accelerated CG (PF-LaCG) algorithm, for which we provide rigorous convergence guarantees. Our theoretical results are complemented by numerical experiments, which demonstrate local acceleration and showcase the practical improvements of PF-LaCG over non-accelerated algorithms, both in terms of iteration count and wall-clock time. Y1 - 2021 ER - TY - JOUR A1 - Bienenstock, Daniel A1 - Muñoz, Gonzalo A1 - Pokutta, Sebastian T1 - Principled Deep Neural Network Training through Linear Programming N2 - Deep Learning has received significant attention due to its impressive performance in many state-of-the-art learning tasks. Unfortunately, while very powerful, Deep Learning is not well understood theoretically and in particular only recently results for the complexity of training deep neural networks have been obtained. In this work we show that large classes of deep neural networks with various architectures (e.g., DNNs, CNNs, Binary Neural Networks, and ResNets), activation functions (e.g., ReLUs and leaky ReLUs), and loss functions (e.g., Hinge loss, Euclidean loss, etc) can be trained to near optimality with desired target accuracy using linear programming in time that is exponential in the input data and parameter space dimension and polynomial in the size of the data set; improvements of the dependence in the input dimension are known to be unlikely assuming P≠NP, and improving the dependence on the parameter space dimension remains open. In particular, we obtain polynomial time algorithms for training for a given fixed network architecture. Our work applies more broadly to empirical risk minimization problems which allows us to generalize various previous results and obtain new complexity results for previously unstudied architectures in the proper learning setting. Y1 - 2018 ER - TY - CHAP A1 - Kerdreux, Thomas A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Projection-Free Optimization on Uniformly Convex Sets T2 - To Appear in Proceedings of AISTATS Y1 - 2020 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian T1 - Second-order Conditional Gradient Sliding N2 - Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the \emph{Second-Order Conditional Gradient Sliding} (SOCGS) algorithm, which uses a projection-free algorithm to solve the constrained quadratic subproblems inexactly. When the feasible region is a polytope the algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. Once in the quadratic regime the SOCGS algorithm requires O(log(log1/ε)) first-order and Hessian oracle calls and O(log(1/ε)log(log1/ε)) linear minimization oracle calls to achieve an ε-optimal solution. This algorithm is useful when the feasible region can only be accessed efficiently through a linear optimization oracle, and computing first-order information of the function, although possible, is costly. Y1 - 2020 ER - TY - JOUR A1 - Kerdreux, Thomas A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Local and Global Uniform Convexity Conditions N2 - We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with scaling inequalities used in analysing the convergence of optimization methods. In particular, we establish local versions of these conditions to provide sharper insights on a recent body of complexity results in learning theory, online learning, or offline optimization, which rely on the strong convexity of the feasible set. While they have a significant impact on complexity, these strong convexity or uniform convexity properties of feasible sets are not exploited as thoroughly as their functional counterparts, and this work is an effort to correct this imbalance. We conclude with some practical examples in optimization and machine learning where leveraging these conditions and localized assumptions lead to new complexity results. Y1 - 2021 ER - TY - JOUR A1 - Bärmann, Andreas A1 - Martin, Alexander A1 - Pokutta, Sebastian A1 - Schneider, Oskar T1 - An Online-Learning Approach to Inverse Optimization Y1 - 2018 ER - TY - CHAP A1 - Parczyk, Olaf A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Szabó, Tibor T1 - New Ramsey Multiplicity Bounds and Search Heuristics T2 - Discrete Mathematics Days N2 - We study two related problems concerning the number of monochromatic cliques in two-colorings of the complete graph that go back to questions of Erdős. Most notably, we improve the 25-year-old upper bounds of Thomason on the Ramsey multiplicity of K4 and K5 and we settle the minimum number of independent sets of size 4 in graphs with clique number at most 4. Motivated by the elusiveness of the symmetric Ramsey multiplicity problem, we also introduce an off-diagonal variant and obtain tight results when counting monochromatic K4 or K5 in only one of the colors and triangles in the other. The extremal constructions for each problem turn out to be blow-ups of a finite graph and were found through search heuristics. They are complemented by lower bounds and stability results established using Flag Algebras, resulting in a fully computer-assisted approach. More broadly, these problems lead us to the study of the region of possible pairs of clique and independent set densities that can be realized as the limit of some sequence of graphs. Y1 - 2022 ER - TY - JOUR A1 - Hunkenschröder, Christoph A1 - Pokutta, Sebastian A1 - Weismantel, Robert T1 - Optimizing a low-dimensional convex function over a high-dimensional cub JF - SIAM Journal on Optimization Y1 - 2022 ER - TY - CHAP A1 - Wäldchen, Stephan A1 - Huber, Felix A1 - Pokutta, Sebastian T1 - Training Characteristic Functions with Reinforcement Learning: XAI-methods Play Connect Four T2 - Proceedings of the International Conference on Machine Learning Y1 - 2022 ER - TY - CHAP A1 - Tsuji, Kazuma A1 - Tanaka, Ken'ichiro A1 - Pokutta, Sebastian T1 - Pairwise Conditional Gradients without Swap Steps and Sparser Kernel Herding T2 - Proceedings of the International Conference on Machine Learning Y1 - 2022 ER - TY - JOUR A1 - Roux, Christophe A1 - Pokutta, Sebastian A1 - Wirth, Elias A1 - Kerdreux, Thomas T1 - Efficient Online-Bandit Strategies for Minimax Learning Problems N2 - Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning [Namkoong and Duchi, 2016, Curi et al., 2020] or learning with non-standard aggregated losses [Shalev- Shwartz and Wexler, 2016, Fan et al., 2017]. More specifically, these problems are convex-linear problems where the minimization is carried out over the model parameters w ∈ W and the maximization over the empirical distribution p ∈ K of the training set indexes, where K is the simplex or a subset of it. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm. We argue that the efficiency of such approaches critically depends on the structure of K and propose two properties of K that facilitate designing efficient algorithms. We focus on a specific family of sets Sn,k encompassing various learning applications and provide high-probability convergence guarantees to the minimax values. Y1 - 2021 ER - TY - JOUR A1 - Kossen, Tabea A1 - Hirzel, Manuel A. A1 - Madai, Vince I. A1 - Boenisch, Franziska A1 - Hennemuth, Anja A1 - Hildebrand, Kristian A1 - Pokutta, Sebastian A1 - Sharma, Kartikey A1 - Hilbert, Adam A1 - Sobesky, Jan A1 - Galinovic, Ivana A1 - Khalil, Ahmed A. A1 - Fiebach, Jochen B. A1 - Frey, Dietmar T1 - Towards Sharing Brain Images: Differentially Private TOF-MRA Images with Segmentation Labels Using Generative Adversarial Networks JF - Frontiers in Artificial Intelligence N2 - Sharing labeled data is crucial to acquire large datasets for various Deep Learning applications. In medical imaging, this is often not feasible due to privacy regulations. Whereas anonymization would be a solution, standard techniques have been shown to be partially reversible. Here, synthetic data using a Generative Adversarial Network (GAN) with differential privacy guarantees could be a solution to ensure the patient's privacy while maintaining the predictive properties of the data. In this study, we implemented a Wasserstein GAN (WGAN) with and without differential privacy guarantees to generate privacy-preserving labeled Time-of-Flight Magnetic Resonance Angiography (TOF-MRA) image patches for brain vessel segmentation. The synthesized image-label pairs were used to train a U-net which was evaluated in terms of the segmentation performance on real patient images from two different datasets. Additionally, the Fréchet Inception Distance (FID) was calculated between the generated images and the real images to assess their similarity. During the evaluation using the U-Net and the FID, we explored the effect of different levels of privacy which was represented by the parameter ϵ. With stricter privacy guarantees, the segmentation performance and the similarity to the real patient images in terms of FID decreased. Our best segmentation model, trained on synthetic and private data, achieved a Dice Similarity Coefficient (DSC) of 0.75 for ϵ = 7.4 compared to 0.84 for ϵ = ∞ in a brain vessel segmentation paradigm (DSC of 0.69 and 0.88 on the second test set, respectively). We identified a threshold of ϵ <5 for which the performance (DSC <0.61) became unstable and not usable. Our synthesized labeled TOF-MRA images with strict privacy guarantees retained predictive properties necessary for segmenting the brain vessels. Although further research is warranted regarding generalizability to other imaging modalities and performance improvement, our results mark an encouraging first step for privacy-preserving data sharing in medical imaging. Y1 - 2022 U6 - https://doi.org/https://doi.org/10.3389/frai.2022.813842 ER - TY - CHAP A1 - Criado, Francisco A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Fast Algorithms for Packing Proportional Fairness and its Dual T2 - Proceedings of the Conference on Neural Information Processing Systems N2 - The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained maximization of sum_i log x_i, is known as the packing proportional fairness problem when the feasible set is defined by positive linear constraints and x ∈ R≥0. In this work, we present a distributed accelerated first-order method for this problem which improves upon previous approaches. We also design an algorithm for the optimization of its dual problem. Both algorithms are width-independent. Y1 - 2022 VL - 36 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - CINDy: Conditional gradient-based Identification of Non-linear Dynamics – Noise-robust recovery JF - Journal of Computational and Applied Mathematics N2 - Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry. Y1 - 2021 ER - TY - JOUR A1 - Combettes, Cyrille A1 - Pokutta, Sebastian T1 - Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm JF - Mathematical Programming Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01735-x VL - 197 SP - 191 EP - 214 ER - TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - An Algorithm-Independent Measure of Progress for Linear Constraint Propagation T2 - 27th International Conference on Principles and Practice of Constraint Programming (CP 2021) N2 - Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure -- independently of the algorithmic design -- the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported. Y1 - 2021 U6 - https://doi.org/10.4230/LIPIcs.CP.2021.52 VL - 210 SP - 52:1 EP - 52:17 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Gleixner, Ambros A1 - Lichocki, Pawel A1 - Pokutta, Sebastian T1 - Online Learning for Scheduling MIP Heuristics T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research N2 - Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on hard-coded rules derived from empirical testing on a large heterogeneous corpora of benchmark instances might lead to sub-optimal performance. In this work, we propose an online learning approach that adapts the application of heuristics towards the single instance at hand. We replace the commonly used static heuristic handling with an adaptive framework exploiting past observations about the heuristic’s behavior to make future decisions. In particular, we model the problem of controlling Large Neighborhood Search and Diving – two broad and complex classes of heuristics – as a multi-armed bandit problem. Going beyond existing work in the literature, we control two different classes of heuristics simultaneously by a single learning agent. We verify our approach numerically and show consistent node reductions over the MIPLIB 2017 Benchmark set. For harder instances that take at least 1000 seconds to solve, we observe a speedup of 4%. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-33271-5_8 VL - 13884 SP - 114 EP - 123 PB - Springer, Cham ER - TY - JOUR A1 - Šofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - An Algorithm-independent Measure of Progress for Linear Constraint Propagation JF - Constraints Y1 - 2022 U6 - https://doi.org/10.1007/s10601-022-09338-9 VL - 27 SP - 432 EP - 455 ER - TY - CHAP A1 - Chmiela, Antonia A1 - Khalil, Elias B. A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Pokutta, Sebastian T1 - Learning to Schedule Heuristics in Branch and Bound T2 - Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021 N2 - Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances. Y1 - 2021 ER - TY - JOUR A1 - Šofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating domain propagation: An efficient GPU-parallel algorithm over sparse matrices JF - Parallel Computing N2 - • Currently, domain propagation in state-of-the-art MIP solvers is single thread only. • The paper presents a novel, efficient GPU algorithm to perform domain propagation. • Challenges are dynamic algorithmic behavior, dependency structures, sparsity patterns. • The algorithm is capable of running entirely on the GPU with no CPU involvement. • We achieve speed-ups of around 10x to 20x, up to 180x on favorably-large instances. Y1 - 2022 U6 - https://doi.org/10.1016/j.parco.2021.102874 VL - 109 SP - 102874 ER - TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices T2 - 2020 IEEE/ACM 10th Workshop on Irregular Applications: Architectures and Algorithms (IA3) N2 - Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 195x on favorably-large instances. Y1 - 2020 U6 - https://doi.org/10.1109/IA351965.2020.00007 N1 - URL of the Slides: https://app.box.com/s/qy0pjmhtbm7shk2ypxjxlh2sj4nudvyu N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/09/20/gpu-prob.html SP - 1 EP - 11 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Wirth, Elias A1 - Pokutta, Sebastian T1 - Accelerated and Sparse Algorithms for Approximate Personalized PageRank and Beyond T2 - Proceedings of Machine Learning Research N2 - It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the ℓ1-regularized undirected personalized PageRank problem (Fountoulakis et al., 2019), leading to cheap iteration complexity and providing the same guarantees as the approximate personalized PageRank algorithm (APPR) (Andersen et al., 2006). In this work, we design an accelerated optimization algorithm for this problem that also performs sparse updates, providing an affirmative answer to the COLT 2022 open question of Fountoulakis and Yang (2022). Acceleration provides a reduced dependence on the condition number, while the dependence on the sparsity in our updates differs from the ISTA approach. Further, we design another algorithm by using conjugate directions to achieve an exact solution while exploiting sparsity. Both algorithms lead to faster convergence for certain parameter regimes. Our findings apply beyond PageRank and work for any quadratic objective whose Hessian is a positive-definite 푀-matrix. Y1 - 2023 UR - https://proceedings.mlr.press/v195/martinez-rubio23a/martinez-rubio23a.pdf VL - 195 SP - 1 EP - 35 ER - TY - CHAP A1 - Parczyk, Olaf A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Szabó, Tibor T1 - Fully Computer-assisted Proofs in Extremal Combinatorics T2 - Proceedings of the AAAI Conference on Artificial Intelligence N2 - We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds. We demonstrate that common search heuristics are capable of finding constructions far beyond the reach of human intuition. Additionally, the most obvious downside of such heuristics, namely a missing guarantee of global optimality, can often be fully eliminated in this case through lower bounds and stability results coming from the Flag Algebra approach. To illustrate the potential of this approach, we study two related and well-known problems in Extremal Graph Theory that go back to questions of Erdős from the 60s. Most notably, we present the first major improvement in the upper bound of the Ramsey multiplicity of the complete graph on 4 vertices in 25 years, precisely determine the first off-diagonal Ramsey multiplicity number, and settle the minimum number of independent sets of size four in graphs with clique number strictly less than five. Y1 - 2023 U6 - https://doi.org/10.1609/aaai.v37i10.26470 VL - 37 IS - 10 SP - 12482 EP - 12490 ER - TY - JOUR A1 - Faenza, Yuri A1 - Muñoz, Gonzalo A1 - Pokutta, Sebastian T1 - New Limits of Treewidth-based tractability in Optimization JF - Mathematical Programming Y1 - 2020 U6 - https://doi.org/10.1007/s10107-020-01563-5 N1 - URL of the PDF: http://link.springer.com/article/10.1007/s10107-020-01563-5 N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2018/09/22/treewidth-abstract.html VL - 191 SP - 559 EP - 594 ER - TY - CHAP A1 - Wirth, Elias A1 - Pokutta, Sebastian T1 - Conditional Gradients for the Approximately Vanishing Ideal T2 - Proceedings of The 25th International Conference on Artificial Intelligence and Statistics N2 - The vanishing ideal of a set of points X is the set of polynomials that evaluate to 0 over all points x in X and admits an efficient representation by a finite set of polynomials called generators. To accommodate the noise in the data set, we introduce the Conditional Gradients Approximately Vanishing Ideal algorithm (CGAVI) for the construction of the set of generators of the approximately vanishing ideal. The constructed set of generators captures polynomial structures in data and gives rise to a feature map that can, for example, be used in combination with a linear classifier for supervised learning. In CGAVI, we construct the set of generators by solving specific instances of (constrained) convex optimization problems with the Pairwise Frank-Wolfe algorithm (PFW). Among other things, the constructed generators inherit the LASSO generalization bound and not only vanish on the training but also on out-sample data. Moreover, CGAVI admits a compact representation of the approximately vanishing ideal by constructing few generators with sparse coefficient vectors. Y1 - 2022 UR - https://proceedings.mlr.press/v151/wirth22a.html VL - 151 SP - 2191 EP - 2209 ER - TY - JOUR A1 - Kerdreux, Thomas A1 - Roux, Christophe A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Linear Bandits on Uniformly Convex Sets JF - Journal of Machine Learning Research N2 - Linear bandit algorithms yield O~(n√T) pseudo-regret bounds on compact convex action sets K⊂Rn and two types of structural assumptions lead to better pseudo-regret bounds. When K is the simplex or an ℓp ball with p∈]1,2], there exist bandits algorithms with O~(√n√T) pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond ℓp balls that enjoy pseudo-regret bounds of O~(√n√T), which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than O(√n). However, this comes at the expense of asymptotic rates in T varying between O(√T) and O(T). Y1 - 2021 UR - https://www.jmlr.org/papers/v22/21-0277.html VL - 22 IS - 284 SP - 1 EP - 23 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penalties T2 - Proceedings of Thirty Sixth Conference on Learning Theory N2 - We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov’s accelerated gradient descent, up to a multiplicative geometric penalty and log factors. Crucially, we can enforce our method to stay within a compact set we define. Prior fully accelerated works \emph{resort to assuming} that the iterates of their algorithms stay in some pre-specified compact set, except for two previous methods of limited applicability. For our manifolds, this solves the open question in (Kim and Yang, 2022) about obtaining global general acceleration without iterates assumptively staying in the feasible set.In our solution, we design an accelerated Riemannian inexact proximal point algorithm, which is a result that was unknown even with exact access to the proximal operator, and is of independent interest. For smooth functions, we show we can implement the prox step inexactly with first-order methods in Riemannian balls of certain diameter that is enough for global accelerated optimization. Y1 - 2023 UR - https://proceedings.mlr.press/v195/martinez-rubio23a.html VL - 195 SP - 359 EP - 393 ER - TY - JOUR A1 - Gelß, Patrick A1 - Klus, Stefan A1 - Knebel, Sebastian A1 - Shakibaei, Zarin A1 - Pokutta, Sebastian T1 - Low-Rank Tensor Decompositions of Quantum Circuits JF - Journal of Computational Physics N2 - Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation, optimization, and physical realization of quantum circuits is of utmost importance for designing novel algorithms. We show how matrix product states (MPSs) and matrix product operators (MPOs) can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers and to gain insight into the underlying structure of the system. We present different examples to demonstrate the advantages of MPO formulations and show that they are more efficient than conventional techniques if the bond dimensions of the wave function representation can be kept small throughout the simulation. Y1 - 2022 ER - TY - CHAP A1 - Dey, Santanu Sabush A1 - Pokutta, Sebastian T1 - Design and verify: a new scheme for generating cutting-planes T2 - Proceedings of IPCO, Lecture Notes in Computer Science Y1 - 2011 UR - http://www.optimization-online.org/DB_HTML/2011/04/3002.html N1 - Additional Note: DOI: 10.1007/978-3-642-20807-2_12 VL - 6655 SP - 143 EP - 155 ER - TY - JOUR A1 - Dey, Santanu Sabush A1 - Pokutta, Sebastian T1 - Design and verify: a new scheme for generating cutting-planes JF - Mathematical Programming A Y1 - 2014 UR - http://www.optimization-online.org/DB_HTML/2011/04/3002.html N1 - Additional Note: DOI: 10.1007/978-3-642-20807-2_12 VL - 145 SP - 199 EP - 222 ER - TY - JOUR A1 - Bienstock, Daniel A1 - Muñoz, Gonzalo A1 - Pokutta, Sebastian T1 - Principled Deep Neural Network Training Through Linear Programming JF - Discrete Optimization N2 - Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident and multiple works in recent years have focused on this task. In this work, using a unified framework, we show that there exists a polyhedron that simultaneously encodes, in its facial structure, all possible deep neural network training problems that can arise from a given architecture, activation functions, loss function, and sample size. Notably, the size of the polyhedral representation depends only linearly on the sample size, and a better dependency on several other network parameters is unlikely. Using this general result, we compute the size of the polyhedral encoding for commonly used neural network architectures. Our results provide a new perspective on training problems through the lens of polyhedral theory and reveal strong structure arising from these problems. Y1 - 2023 U6 - https://doi.org/10.1016/j.disopt.2023.100795 VL - 49 ER - TY - JOUR A1 - Kevin-Martin, Aigner A1 - Bärmann, Andreas A1 - Braun, Kristin A1 - Liers, Frauke A1 - Pokutta, Sebastian A1 - Schneider, Oskar A1 - Sharma, Kartikey A1 - Tschuppik, Sebastian T1 - Data-driven Distributionally Robust Optimization over Time JF - INFORMS Journal on Optimization N2 - Stochastic optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. Because the latter is often unknown, distributionally robust optimization (DRO) provides a strong alternative that determines the best guaranteed solution over a set of distributions (ambiguity set). In this work, we present an approach for DRO over time that uses online learning and scenario observations arriving as a data stream to learn more about the uncertainty. Our robust solutions adapt over time and reduce the cost of protection with shrinking ambiguity. For various kinds of ambiguity sets, the robust solutions converge to the SO solution. Our algorithm achieves the optimization and learning goals without solving the DRO problem exactly at any step. We also provide a regret bound for the quality of the online strategy that converges at a rate of O(log T/T−−√), where T is the number of iterations. Furthermore, we illustrate the effectiveness of our procedure by numerical experiments on mixed-integer optimization instances from popular benchmark libraries and give practical examples stemming from telecommunications and routing. Our algorithm is able to solve the DRO over time problem significantly faster than standard reformulations. Y1 - 2023 U6 - https://doi.org/10.1287/ijoo.2023.0091 VL - 5 IS - 4 SP - 376 EP - 394 ER - TY - CHAP A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Mathieu, Besançon T1 - Simple steps are all you need: Frank-Wolfe and generalized self-concordant functions T2 - Thirty-fifth Conference on Neural Information Processing Systems, NeurIPS 2021 N2 - Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy 𝛾𝑡 = 2/(𝑡 + 2), obtaining a O (1/𝑡) convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where 𝑡 is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral. Y1 - 2021 ER - TY - JOUR A1 - Mathieu, Besançon A1 - Carderera, Alejandro A1 - Pokutta, Sebastian T1 - FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients JF - INFORMS Journal on Computing N2 - We present FrankWolfe.jl, an open-source implementation of several popular Frank–Wolfe and conditional gradients variants for first-order constrained optimization. The package is designed with flexibility and high performance in mind, allowing for easy extension and relying on few assumptions regarding the user-provided functions. It supports Julia’s unique multiple dispatch feature, and it interfaces smoothly with generic linear optimization formulations using MathOptInterface.jl. Y1 - 2022 U6 - https://doi.org/10.1287/ijoc.2022.1191 VL - 34 IS - 5 SP - 2383 EP - 2865 ER - TY - CHAP A1 - MacDonald, Jan A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings T2 - Proceedings of the International Conference on Machine Learning Y1 - 2022 ER - TY - JOUR A1 - Designolle, Sébastien A1 - Besançon, Mathieu A1 - Iommazzo, Gabriele A1 - Knebel, Sebastian A1 - Gelß, Patrick A1 - Pokutta, Sebastian T1 - Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms JF - Physical Review Research N2 - In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope: Constructing local models and deriving separating hyperplanes, that is, Bell inequalities. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. First, we study the threshold value for the nonlocality of two-qubit Werner states under projective measurements. Here, we improve on both the upper and lower bounds present in the literature. Importantly, our bounds are entirely analytical; moreover, they yield refined bounds on the value of the Grothendieck constant of order three: 1.4367⩽KG(3)⩽1.4546. Second, we demonstrate the efficiency of our approach in multipartite Bell scenarios, and present local models for all projective measurements with visibilities noticeably higher than the entanglement threshold. We make our entire code accessible as a julia library called BellPolytopes.jl. Y1 - 2023 U6 - https://doi.org/10.1103/PhysRevResearch.5.043059 VL - 5 SP - 043059 ER - TY - CHAP A1 - Wirth, Elias A1 - Kerdreux, Thomas A1 - Pokutta, Sebastian T1 - Acceleration of Frank-Wolfe Algorithms with Open Loop Step-sizes T2 - Proceedings of International Conference on Artificial Intelligence and Statistics Y1 - 2023 ER - TY - CHAP A1 - Zimmer, Max A1 - Spiegel, Christoph A1 - Pokutta, Sebastian T1 - How I Learned to Stop Worrying and Love Retraining T2 - Proceedings of International Conference on Learning Representations Y1 - 2023 ER - TY - JOUR A1 - Pokutta, Sebastian T1 - The Frank-Wolfe algorithm: a short introduction JF - Jahresbericht der Deutschen Mathematiker-Vereinigung Y1 - 2023 ER - TY - CHAP A1 - Zimmer, Max A1 - Spiegel, Christoph A1 - Pokutta, Sebastian T1 - Sparse Model Soups T2 - Proceedings of International Conference on Learning Representations Y1 - 2024 ER - TY - JOUR A1 - Designolle, Sébastien A1 - Iommazzo, Gabriele A1 - Besançon, Mathieu A1 - Knebel, Sebastian A1 - Gelß, Patrick A1 - Pokutta, Sebastian T1 - Improved local models and new Bell inequalities via Frank-Wolfe algorithms JF - Physical Review Research N2 - In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope: Constructing local models and deriving separating hyperplanes, that is, Bell inequalities. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. First, we study the threshold value for the nonlocality of two-qubit Werner states under projective measurements. Here, we improve on both the upper and lower bounds present in the literature. Importantly, our bounds are entirely analytical; moreover, they yield refined bounds on the value of the Grothendieck constant of order three: 1.4367⩽KG(3)⩽1.4546. Second, we demonstrate the efficiency of our approach in multipartite Bell scenarios, and present local models for all projective measurements with visibilities noticeably higher than the entanglement threshold. We make our entire code accessible as a julia library called BellPolytopes.jl. Y1 - 2023 U6 - https://doi.org/10.1103/PhysRevResearch.5.043059 VL - 5 SP - 043059 ER - TY - CHAP A1 - Gasse, Maxime A1 - Bowly, Simon A1 - Cappart, Quentin A1 - Charfreitag, Jonas A1 - Charlin, Laurent A1 - Chételat, Didier A1 - Chmiela, Antonia A1 - Dumouchelle, Justin A1 - Gleixner, Ambros A1 - Kazachkov, Aleksandr M. A1 - Khalil, Elias A1 - Lichocki, Pawel A1 - Lodi, Andrea A1 - Lubin, Miles A1 - Maddison, Chris J. A1 - Christopher, Morris A1 - Papageorgiou, Dimitri J. A1 - Parjadis, Augustin A1 - Pokutta, Sebastian A1 - Prouvost, Antoine A1 - Scavuzzo, Lara A1 - Zarpellon, Giulia A1 - Yang, Linxin A1 - Lai, Sha A1 - Wang, Akang A1 - Luo, Xiaodong A1 - Zhou, Xiang A1 - Huang, Haohan A1 - Shao, Shengcheng A1 - Zhu, Yuanming A1 - Zhang, Dong A1 - Quan, Tao A1 - Cao, Zixuan A1 - Xu, Yang A1 - Huang, Zhewei A1 - Zhou, Shuchang A1 - Binbin, Chen A1 - Minggui, He A1 - Hao, Hao A1 - Zhiyu, Zhang A1 - Zhiwu, An A1 - Kun, Mao T1 - The Machine Learning for Combinatorial Optimization Competition (ML4CO): results and insights T2 - Proceedings of Conference on Neural Information Processing Systems Y1 - 2022 ER - TY - CHAP A1 - Wirth, Elias A1 - Kera, A1 - Pokutta, Sebastian T1 - Approximate Vanishing Ideal Computations at Scale T2 - Proceedings of International Conference on Learning Representations Y1 - 2023 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Roux, Christophe A1 - Criscitiello, Christopher A1 - Pokutta, Sebastian T1 - Accelerated Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties T2 - Proceedings of Optimization for Machine Learning (NeurIPS Workshop OPT 2023) Y1 - 2023 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Accelerated Riemannian optimization: Handling constraints with a prox to bound geometric penalties T2 - Proceedings of Optimization for Machine Learning (NeurIPS Workshop OPT 2022) Y1 - 2022 ER - TY - JOUR A1 - Hunkenschröder, Christoph A1 - Pokutta, Sebastian A1 - Weismantel, Robert T1 - Optimizing a low-dimensional convex function over a high-dimensional cube JF - SIAM Journal on Optimization Y1 - 2022 ER - TY - CHAP A1 - Thuerck, Daniel A1 - Sofranac, Boro A1 - Pfetsch, Marc A1 - Pokutta, Sebastian T1 - Learning cuts via enumeration oracles T2 - Proceedings of Conference on Neural Information Processing Systems Y1 - 2023 ER - TY - CHAP A1 - Sharma, Kartikey A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Network Design for the Traffic Assignment Problem with Mixed-Integer Frank-Wolfe T2 - Proceedings of INFORMS Optimization Society Conference Y1 - 2024 ER - TY - JOUR A1 - Kreimeier, Timo A1 - Pokutta, Sebastian A1 - Walther, Andrea A1 - Woodstock, Zev T1 - On a Frank-Wolfe approach for abs-smooth functions JF - Optimization Methods and Software Y1 - U6 - https://doi.org/10.1080/10556788.2023.2296985 ER - TY - JOUR A1 - Designolle, Sébastien A1 - Vértesi, Tamás A1 - Pokutta, Sebastian T1 - Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms JF - Physics Review A N2 - In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrized local polytope and they give the best-known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalize our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to the activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements. Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevA.109.022205 VL - 109 IS - 2 ER - TY - JOUR A1 - Deza, Antoine A1 - Pokutta, Sebastian A1 - Pournin, Lionel T1 - The complexity of geometric scaling JF - Operations Research Letters Y1 - 2024 U6 - https://doi.org/10.1016/j.orl.2023.11.010 VL - 52 SP - 107057 ER - TY - JOUR A1 - Braun, Gábor A1 - Guzmán, Cristóbal A1 - Pokutta, Sebastian T1 - Corrigendum in “Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization via Information Theory” JF - IEEE Transactions on Information Theory Y1 - 2024 U6 - https://doi.org/10.1109/TIT.2024.3357200 ER - TY - CHAP A1 - Wäldchen, Stephan A1 - Sharma, Kartikey A1 - Turan, Berkant A1 - Zimmer, Max A1 - Pokutta, Sebastian T1 - Interpretability Guarantees with Merlin-Arthur Classifiers T2 - Proceedings of International Conference on Artificial Intelligence and Statistics N2 - We propose an interactive multi-agent classifier that provides provable interpretability guarantees even for complex agents such as neural networks. These guarantees consist of lower bounds on the mutual information between selected features and the classification decision. Our results are inspired by the Merlin-Arthur protocol from Interactive Proof Systems and express these bounds in terms of measurable metrics such as soundness and completeness. Compared to existing interactive setups, we rely neither on optimal agents nor on the assumption that features are distributed independently. Instead, we use the relative strength of the agents as well as the new concept of Asymmetric Feature Correlation which captures the precise kind of correlations that make interpretability guarantees difficult. We evaluate our results on two small-scale datasets where high mutual information can be verified explicitly. Y1 - 2024 ER -