@inproceedings{BuiCombettesWoodstock2022, author = {B{\´u}i, M. N. and Combettes, P. L. and Woodstock, Zev}, title = {block-activated algorithms for multicomponent fully nonsmooth minimization}, booktitle = {Proceedings of ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year = {2022}, language = {en} } @article{BolusaniRalphs2022, author = {Bolusani, Suresh and Ralphs, Ted K.}, title = {a framework for generalized Benders' decomposition and its applications to multilevel optimization}, journal = {Mathematical Programming}, year = {2022}, language = {en} } @article{WilkenBesanconKratochviletal.2022, author = {Wilken, St. Elmo and Besan{\c{c}}on, Mathieu and Kratochv{\´i}l, Miroslav and Kuate, Chilperic Armel Foko and Trefois, Christophe and Gu, Wei and Ebenh{\"o}h, Oliver}, title = {Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models}, journal = {Metabolic Engineering}, year = {2022}, language = {en} } @inproceedings{CombettesWoodstock2022, author = {Combettes, P. L. and Woodstock, Zev}, title = {signal recovery from inconsistent nonlinear observations}, booktitle = {Proceedings of ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year = {2022}, language = {en} } @article{HintermuellerStengl2024, author = {Hinterm{\"u}ller, Michael and Stengl, Steven-Marian}, title = {A Generalized 𝛤-Convergence Concept for a Class of Equilibrium Problems}, volume = {34}, journal = {Journal of Nonlinear Science}, number = {83}, doi = {10.1007/s00332-024-10059-x}, year = {2024}, language = {en} } @article{StenglGelssKlusetal.2024, author = {Stengl, Steven-Marian and Gelß, Patrick and Klus, Stefan and Pokutta, Sebastian}, title = {Existence and uniqueness of solutions of the Koopman--von Neumann equation on bounded domains}, volume = {57}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {39}, doi = {10.1088/1751-8121/ad6f7d}, year = {2024}, language = {en} } @article{BoettcherParczykSguegliaetal.2024, author = {B{\"o}ttcher, Julia and Parczyk, Olaf and Sgueglia, Amedeo and Skokan, Jozef}, title = {The square of a Hamilton cycle in randomly perturbed graphs}, volume = {65}, journal = {Random Structures \& Algorithms}, number = {2}, doi = {10.1002/rsa.21215}, pages = {342 -- 386}, year = {2024}, language = {en} } @article{DezaOnnPokuttaetal.2024, author = {Deza, Antoine and Onn, Shmuel and Pokutta, Sebastian and Pournin, Lionel}, title = {Kissing polytopes}, volume = {38}, journal = {SIAM Journal on Discrete Mathematics}, number = {4}, doi = {10.1137/24M1640859}, year = {2024}, abstract = {We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.}, language = {en} } @article{HartzerRoehrigWolffetal.2022, author = {Hartzer, Jacob and R{\"o}hrig, Olivia and Wolff, Timo and Y{\"u}r{\"u}k, Oğuzhan}, title = {Initial steps in the classification of maximal mediated sets}, journal = {Journal of Symbolic Computation}, year = {2022}, language = {en} } @article{Kerdreuxd'AspremontPokutta2022, author = {Kerdreux, Thomas and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Restarting Frank-Wolfe: Faster Rates under H{\"o}lderian Error Bounds}, journal = {Journal of Optimization Theory and Applications}, year = {2022}, language = {en} } @article{CombettesPokutta2023, author = {Combettes, Cyrille and Pokutta, Sebastian}, title = {Revisiting the Approximate Carath{\´e}odory Problem via the Frank-Wolfe Algorithm}, volume = {197}, journal = {Mathematical Programming A}, doi = {10.1007/s10107-021-01735-x}, pages = {191 -- 214}, year = {2023}, language = {en} } @article{GelssIssagaliKornhuber2024, author = {Gelß, Patrick and Issagali, Aizhan and Kornhuber, Ralf}, title = {Fredholm integral equations for function approximation and the training of neural networks}, volume = {6}, journal = {SIAM Journal on Mathematics of Data Science}, number = {4}, doi = {10.1137/23M156642X}, year = {2024}, language = {en} } @article{Stengl2024, author = {Stengl, Steven-Marian}, title = {An alternative formulation of the quantum phase estimation using projection-based tensor decompositions}, volume = {23}, journal = {Quantum Information Processing}, doi = {10.1007/s11128-024-04347-4}, year = {2024}, language = {en} } @article{Vu‐HanSunkaraBermudez‐Schettinoetal.2025, author = {Vu-Han, Tu-Lan and Sunkara, Vikram and Bermudez-Schettino, Rodrigo and Schwechten, Jakob and Runge, Robin and Perka, Carsten and Winkler, Tobias and Pokutta, Sebastian and Weiß, Claudia and Pumberger, Matthias}, title = {Feature Engineering for the Prediction of Scoliosis in 5q-Spinal Muscular Atrophy}, volume = {16}, journal = {Journal of Cachexia, Sarcopenia and Muscle}, number = {1}, doi = {10.1002/jcsm.13599}, pages = {e13599}, year = {2025}, language = {en} } @inproceedings{KeraIshiharaKambeetal.2024, author = {Kera, Hiroshi and Ishihara, Yuki and Kambe, Yuta and Vaccon, Tristan and Yokoyama, Kazuhiro}, title = {Learning to Compute Gr\"obner Bases}, booktitle = {Proceedings of the Conference on Neural Information Processing Systems}, year = {2024}, language = {en} } @inproceedings{KumanoKeraYamasaki2024, author = {Kumano, Soichiro and Kera, Hiroshi and Yamasaki, Toshihiko}, title = {Wide Two-Layer Networks can Learn from Adversarial Perturbations}, booktitle = {Proceedings of the Conference on Neural Information Processing Systems}, year = {2024}, language = {en} } @inproceedings{TroppensBesanconWilkenetal.2025, author = {Troppens, Hannah and Besan{\c{c}}on, Mathieu and Wilken, St. Elmo and Pokutta, Sebastian}, title = {Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks}, volume = {338}, booktitle = {23rd International Symposium on Experimental Algorithms (SEA 2025)}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.SEA.2025.26}, pages = {26:1 -- 26:18}, year = {2025}, language = {en} } @inproceedings{GłuchTuranNagarajanetal.2025, author = {Głuch, Grzegorz and Turan, Berkant and Nagarajan, Sai Ganesh and Pokutta, Sebastian}, title = {The good, the bad and the ugly: watermarks, transferable attacks and adversarial defenses}, booktitle = {1st Workshop on GenAI Watermarking, collocated with ICLR 2025}, year = {2025}, language = {en} } @inproceedings{HollenderMaystreNagarajan2025, author = {Hollender, Alexandros and Maystre, Gilbert and Nagarajan, Sai Ganesh}, title = {The Complexity of Two-Team Polymatrix Games with Independent Adversaries}, booktitle = {13th International Conference on Learning Representations (ICLR 2025)}, arxiv = {http://arxiv.org/abs/2409.07398}, year = {2025}, abstract = {Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding the limits of tractability in polymatrix games, we study the computation of Nash equilibria in such games where each pair of players plays either a zero-sum or a coordination game. We are particularly interested in the setting where players can be grouped into a small number of teams of identical interest. While the three-team version of the problem is known to be PPAD-complete, the complexity for two teams has remained open. Our main contribution is to prove that the two-team version remains hard, namely it is CLS-hard. Furthermore, we show that this lower bound is tight for the setting where one of the teams consists of multiple independent adversaries. On the way to obtaining our main result, we prove hardness of finding any stationary point in the simplest type of non-convex-concave min-max constrained optimization problem, namely for a class of bilinear polynomial objective functions.}, language = {en} } @inproceedings{BesanconPokuttaWirth2025, author = {Besan{\c{c}}on, Mathieu and Pokutta, Sebastian and Wirth, Elias}, title = {The Pivoting Framework: Frank-Wolfe Algorithms with Active Set Size Control}, volume = {258}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {271 -- 279}, year = {2025}, language = {en} } @inproceedings{MartinezRubioRouxCriscitielloetal.2025, author = {Mart{\´i}nez-Rubio, David and Roux, Christophe and Criscitiello, Christopher and Pokutta, Sebastian}, title = {Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties}, volume = {258}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {280 -- 288}, year = {2025}, language = {en} } @inproceedings{SadikuWagnerPokutta2025, author = {Sadiku, Shpresim and Wagner, Moritz and Pokutta, Sebastian}, title = {GSE: Group-wise sparse and explainable adversarial attacks}, booktitle = {13th International Conference on Learning Representations (ICLR 2025)}, arxiv = {http://arxiv.org/abs/2311.17434}, year = {2025}, language = {en} } @article{WirthPenaPokutta2025, author = {Wirth, Elias and Pena, Javier and Pokutta, Sebastian}, title = {Correction: Accelerated affine-invariant convergence rates of the Frank-Wolfe algorithm with open-loop step-sizes}, volume = {214}, journal = {Mathematical Programming}, doi = {10.1007/s10107-025-02214-3}, pages = {941 -- 942}, year = {2025}, language = {en} } @inproceedings{RouxZimmerPokutta2025, author = {Roux, Christophe and Zimmer, Max and Pokutta, Sebastian}, title = {On the byzantine-resilience of distillation-based federated learning}, booktitle = {13th International Conference on Learning Representations (ICLR 2025)}, arxiv = {http://arxiv.org/abs/2402.12265}, year = {2025}, abstract = {Federated Learning (FL) algorithms using Knowledge Distillation (KD) have received increasing attention due to their favorable properties with respect to privacy, non-i.i.d. data and communication cost. These methods depart from transmitting model parameters and instead communicate information about a learning task by sharing predictions on a public dataset. In this work, we study the performance of such approaches in the byzantine setting, where a subset of the clients act in an adversarial manner aiming to disrupt the learning process. We show that KD-based FL algorithms are remarkably resilient and analyze how byzantine clients can influence the learning process. Based on these insights, we introduce two new byzantine attacks and demonstrate their ability to break existing byzantine-resilient methods. Additionally, we propose a novel defence method which enhances the byzantine resilience of KD-based FL algorithms. Finally, we provide a general framework to obfuscate attacks, making them significantly harder to detect, thereby improving their effectiveness.}, language = {en} } @inproceedings{SadikuWagnerNagarajanetal.2025, author = {Sadiku, Shpresim and Wagner, Moritz and Nagarajan, Sai Ganesh and Pokutta, Sebastian}, title = {S-CFE: Simple Counterfactual Explanations}, volume = {258}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {172 -- 180}, year = {2025}, language = {en} } @inproceedings{BestuzhevaGleixnerAchterberg2023, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Achterberg, Tobias}, title = {Efficient Separation of RLT Cuts for Implicit and Explicit Bilinear Products}, volume = {13904}, booktitle = {Integer Programming and Combinatorial Optimization. IPCO 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-32726-1_2}, pages = {14 -- 28}, year = {2023}, abstract = {The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and improve the performance of RLT for bilinear product relations. First, a method for detecting bilinear product relations implicitly contained in mixed-integer linear programs is developed based on analyzing linear constraints with binary variables, thus enabling the application of bilinear RLT to a new class of problems. Our second contribution addresses the high computational cost of RLT cut separation, which presents one of the major difficulties in applying RLT efficiently in practice. We propose a new RLT cutting plane separation algorithm which identifies combinations of linear constraints and bound factors that are expected to yield an inequality that is violated by the current relaxation solution. A detailed computational study based on implementations in two solvers evaluates the performance impact of the proposed methods.}, language = {en} } @inproceedings{MexiBertholdGleixneretal.2023, author = {Mexi, Gioni and Berthold, Timo and Gleixner, Ambros and Nordstr{\"o}m, Jakob}, title = {Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning}, volume = {280}, booktitle = {29th International Conference on Principles and Practice of Constraint Programming (CP 2023)}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.CP.2023.27}, pages = {27:1 -- 27:19}, year = {2023}, abstract = {Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in so-called pseudo-Boolean solving, where solvers can reason directly with 0-1 integer linear inequalities rather than with clausal constraints extracted from such inequalities. In this work, we investigate how pseudo-Boolean conflict analysis can be integrated in MIP solving, focusing on 0-1 integer linear programs (0-1 ILPs). Phrased in MIP terminology, conflict analysis can be understood as a sequence of linear combinations and cuts. We leverage this perspective to design a new conflict analysis algorithm based on mixed integer rounding (MIR) cuts, which theoretically dominates the state-of-the-art division-based method in pseudo-Boolean solving. We also report results from a first proof-of-concept implementation of different pseudo-Boolean conflict analysis methods in the open-source MIP solver SCIP. When evaluated on a large and diverse set of 0-1 ILP instances from MIPLIB2017, our new MIR-based conflict analysis outperforms both previous pseudo-Boolean methods and the clause-based method used in MIP. Our conclusion is that pseudo-Boolean conflict analysis in MIP is a promising research direction that merits further study, and that it might also make sense to investigate the use of such conflict analysis to generate stronger no-goods in constraint programming.}, language = {en} } @inproceedings{MartinezRubioWirthPokutta2023, author = {Mart{\´i}nez-Rubio, David and Wirth, Elias and Pokutta, Sebastian}, title = {Accelerated and Sparse Algorithms for Approximate Personalized PageRank and Beyond}, volume = {195}, booktitle = {Proceedings of Machine Learning Research}, pages = {1 -- 35}, year = {2023}, abstract = {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.}, language = {en} } @inproceedings{RuePernaSpiegel2023, author = {Ru{\´e} Perna, Juanjo and Spiegel, Christoph}, title = {The Rado Multiplicity Problem in Vector Spaces Over Finite Fields}, booktitle = {Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB'23}, doi = {10.5817/CZ.MUNI.EUROCOMB23-108}, pages = {784 -- 789}, year = {2023}, language = {en} } @article{BestuzhevaGleixnerVigerske2023, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Vigerske, Stefan}, title = {A Computational Study of Perspective Cuts}, volume = {15}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-023-00246-4}, pages = {703 -- 731}, year = {2023}, abstract = {The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time.}, language = {en} } @article{KevinMartinBaermannBraunetal.2023, author = {Kevin-Martin, Aigner and B{\"a}rmann, Andreas and Braun, Kristin and Liers, Frauke and Pokutta, Sebastian and Schneider, Oskar and Sharma, Kartikey and Tschuppik, Sebastian}, title = {Data-driven Distributionally Robust Optimization over Time}, volume = {5}, journal = {INFORMS Journal on Optimization}, number = {4}, doi = {10.1287/ijoo.2023.0091}, pages = {376 -- 394}, year = {2023}, abstract = {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.}, language = {en} } @article{RiedelGelssKleinetal.2023, author = {Riedel, Jerome and Gelß, Patrick and Klein, Rupert and Schmidt, Burkhard}, title = {WaveTrain: a Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains}, volume = {158}, journal = {The Journal of Chemical Physics}, number = {16}, doi = {10.1063/5.0147314}, pages = {164801}, year = {2023}, abstract = {WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schr{\"o}dinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.}, language = {en} } @article{CombettesPokutta2023, author = {Combettes, Cyrille and Pokutta, Sebastian}, title = {Revisiting the Approximate Carath{\´e}odory Problem via the Frank-Wolfe Algorithm}, volume = {197}, journal = {Mathematical Programming}, doi = {10.1007/s10107-021-01735-x}, pages = {191 -- 214}, year = {2023}, language = {en} } @inproceedings{XuMexiBestuzheva2025, author = {Xu, Liding and Mexi, Gioni and Bestuzheva, Ksenia}, title = {Sparsity-driven Aggregation of Mixed Integer Programs}, volume = {338}, booktitle = {23rd International Symposium on Experimental Algorithms (SEA 2025)}, address = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.SEA.2025.27}, pages = {27:1 -- 27:15}, year = {2025}, language = {en} } @misc{OPUS4-10176, title = {Mathematical Optimization for Machine Learning}, editor = {Fackeldey, Konstantin and Kannan, Aswin and Pokutta, Sebastian and Sharma, Kartikey and Walter, Daniel and Walter, Andrea and Weiser, Martin}, publisher = {De Gruyter}, isbn = {9783111376776}, doi = {10.1515/9783111376776}, year = {2025}, abstract = {Mathematical optimization and machine learning are closely related. This proceedings volume of the Thematic Einstein Semester 2023 of the Berlin Mathematics Research Center MATH+ collects recent progress on their interplay in topics such as discrete optimization, nonlinear programming, optimal control, first-order methods, multilevel optimization, machine learning in optimization, physics-informed learning, and fairness in machine learning.}, language = {en} } @article{RamosKuehn2022, author = {Ramos, Alejandro and K{\"u}hn, Oliver}, title = {Manipulating the dynamics of a Fermi resonance with light. A direct optimal control theory approach}, journal = {Chemical Physics}, year = {2022}, language = {en} } @incollection{ZimmerSpiegelPokutta2025, author = {Zimmer, Max and Spiegel, Christoph and Pokutta, Sebastian}, title = {Compression-aware training of neural networks using Frank-Wolfe}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, K.}, publisher = {De Gruyter}, doi = {10.1515/9783111376776-010}, pages = {137 -- 168}, year = {2025}, language = {en} } @inproceedings{UrbanoRomero2024, author = {Urbano, Alonso and Romero, David W.}, title = {Self-Supervised Detection of Perfect and Partial Input-Dependent Symmetries}, booktitle = {Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) at ICML 2024}, year = {2024}, language = {en} } @article{RamosFischerSaalfranketal.2024, author = {Ramos, Alejandro and Fischer, Eric W. and Saalfrank, Peter and K{\"u}hn, Oliver}, title = {Shaping the laser control landscape of a hydrogen transfer reaction by vibrational strong coupling. A direct optimal control approach}, journal = {The Journal of Chemical Physics}, year = {2024}, language = {en} } @article{GemanderChenWeningeretal.2020, author = {Gemander, Patrick and Chen, Wei-Kun and Weninger, Dieter and Gottwald, Leona and Gleixner, Ambros}, title = {Two-row and two-column mixed-integer presolve using hashing-based pairing methods}, volume = {8}, journal = {EURO Journal on Computational Optimization}, number = {3-4}, doi = {10.1007/s13675-020-00129-6}, pages = {205 -- 240}, year = {2020}, abstract = {In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.}, language = {en} } @article{BaermannMartinPokuttaetal.2018, author = {B{\"a}rmann, Andreas and Martin, Alexander and Pokutta, Sebastian and Schneider, Oskar}, title = {An Online-Learning Approach to Inverse Optimization}, year = {2018}, language = {en} } @inproceedings{CardereraDiakonikolasLinetal.2021, author = {Carderera, Alejandro and Diakonikolas, Jelena and Lin, Cheuk Yin and Pokutta, Sebastian}, title = {Parameter-free Locally Accelerated Conditional Gradients}, booktitle = {ICML 2021}, year = {2021}, abstract = {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.}, language = {en} } @article{BienenstockMunozPokutta2018, author = {Bienenstock, Daniel and Mu{\~n}oz, Gonzalo and Pokutta, Sebastian}, title = {Principled Deep Neural Network Training through Linear Programming}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{Kerdreuxd'AspremontPokutta2020, author = {Kerdreux, Thomas and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Projection-Free Optimization on Uniformly Convex Sets}, booktitle = {To Appear in Proceedings of AISTATS}, year = {2020}, language = {en} } @article{RouxPokuttaWirthetal.2021, author = {Roux, Christophe and Pokutta, Sebastian and Wirth, Elias and Kerdreux, Thomas}, title = {Efficient Online-Bandit Strategies for Minimax Learning Problems}, year = {2021}, abstract = {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.}, language = {en} } @article{KerdreuxRouxd'Aspremontetal.2021, author = {Kerdreux, Thomas and Roux, Christophe and d'Aspremont, Alexandre and Pokutta, Sebastian}, title = {Linear Bandits on Uniformly Convex Sets}, volume = {22}, journal = {Journal of Machine Learning Research}, number = {284}, pages = {1 -- 23}, year = {2021}, abstract = {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, \S5.5.]. 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).}, language = {en} } @article{NohadaniSharma2022, author = {Nohadani, Omid and Sharma, Kartikey}, title = {Optimization under Connected Uncertainty}, volume = {4}, journal = {INFORMS Journal on Optimization}, number = {3}, doi = {10.1287/ijoo.2021.0067}, pages = {326 -- 346}, year = {2022}, abstract = {Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multiperiod settings. Current approaches model uncertainty either independent of the past or in an implicit fashion by budgeting the aggregate uncertainty. In many applications, however, past realizations directly influence future uncertainties. For this class of problems, we develop a modeling framework that explicitly incorporates this dependence via connected uncertainty sets, whose parameters at each period depend on previous uncertainty realizations. To find optimal here-and-now solutions, we reformulate robust and distributionally robust constraints for popular set structures and demonstrate this modeling framework numerically on broadly applicable knapsack and portfolio-optimization problems.}, language = {en} } @article{GelssKleinMateraetal.2022, author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard}, title = {Solving the time-independent Schr{\"o}dinger equation for chains of coupled excitons and phonons using tensor trains}, volume = {156}, journal = {The Journal of Chemical Physics}, number = {2}, arxiv = {http://arxiv.org/abs/2109.15104}, doi = {10.1063/5.0074948}, pages = {024109}, year = {2022}, abstract = {We demonstrate how to apply the tensor-train format to solve the time-independent Schr{\"o}dinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fr{\"o}hlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fr{\"o}hlich-Holstein type Hamiltonians.}, language = {en} } @article{GelssKlusKnebeletal.2022, author = {Gelß, Patrick and Klus, Stefan and Knebel, Sebastian and Shakibaei, Zarin and Pokutta, Sebastian}, title = {Low-Rank Tensor Decompositions of Quantum Circuits}, journal = {Journal of Computational Physics}, arxiv = {http://arxiv.org/abs/2205.09882}, year = {2022}, abstract = {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.}, language = {en} } @article{EiflerGleixner2023, author = {Eifler, Leon and Gleixner, Ambros}, title = {Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework}, volume = {34}, journal = {SIAM Journal on Optimization}, number = {1}, doi = {10.1137/23M156046X}, year = {2023}, abstract = {This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5\% more instances and reduce solving times by 26.8\% on the MIPLIB 2017 benchmark test set.}, language = {en} }