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 - 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 - 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 - 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 - JOUR A1 - Abbas, Amira A1 - Ambainis, Andris A1 - Augustino, Brandon A1 - Bärtschi, Andreas A1 - Buhrman, Harry A1 - Coffrin, Carleton A1 - Cortiana, Giorgio A1 - Dunjko, Vedran A1 - Egger, Daniel J. A1 - Elmegreen, Bruce G. A1 - Franco, Nicola A1 - Fratini, Filippo A1 - Fuller, Bryce A1 - Gacon, Julien A1 - Gonciulea, Constantin A1 - Gribling, Sander A1 - Gupta, Swati A1 - Hadfield, Stuart A1 - Heese, Raoul A1 - Kircher, Gerhard A1 - Kleinert, Thomas A1 - Koch, Thorsten A1 - Korpas, Georgios A1 - Lenk, Steve A1 - Marecek, Jakub A1 - Markov, Vanio A1 - Mazzola, Guglielmo A1 - Mensa, Stefano A1 - Mohseni, Naeimeh A1 - Nannicini, Giacomo A1 - O’Meara, Corey A1 - Tapia, Elena Peña A1 - Pokutta, Sebastian A1 - Proissl, Manuel A1 - Rebentrost, Patrick A1 - Sahin, Emre A1 - Symons, Benjamin C. B. A1 - Tornow, Sabine A1 - Valls, Víctor A1 - Woerner, Stefan A1 - Wolf-Bauwens, Mira L. A1 - Yard, Jon A1 - Yarkoni, Sheir A1 - Zechiel, Dirk A1 - Zhuk, Sergiy A1 - Zoufal, Christa T1 - Challenges and opportunities in quantum optimization JF - Nature Reviews Physics Y1 - 2024 U6 - https://doi.org/10.1038/s42254-024-00770-9 SN - 2522-5820 VL - 6 SP - 718 EP - 735 PB - Springer Science and Business Media LLC 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - CHAP A1 - Głuch, Grzegorz A1 - Turan, Berkant A1 - Nagarajan, Sai Ganesh A1 - Pokutta, Sebastian T1 - The Good, the Bad and the Ugly: Meta-Analysis of Watermarks, Transferable Attacks and Adversarial Defenses T2 - Proceedings of the Conference on Neural Information Processing Systems Y1 - 2025 ER - TY - CHAP A1 - Kera, Hiroshi A1 - Pelleriti, Nico A1 - Ishihara, Yuki A1 - Zimmer, Max A1 - Pokutta, Sebastian T1 - Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithms T2 - Proceedings of the Conference on Neural Information Processing Systems Y1 - 2025 ER - TY - JOUR A1 - Hendrych, Deborah A1 - Troppens, Hannah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Convex mixed-integer optimization with Frank-Wolfe methods JF - Mathematical Programming Computation Y1 - 2025 U6 - https://doi.org/10.1007/s12532-025-00288-w VL - 17 SP - 731 EP - 757 ER - TY - CHAP A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Secant line search for Frank-Wolfe algorithms T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/hendrych25a/hendrych25a.pdf VL - 267 SP - 23005 EP - 23029 ER - TY - CHAP A1 - Pauls, Jan A1 - Zimmer, Max A1 - Turan, Berkant A1 - Saatchi, Sassan A1 - Ciais, Philippe A1 - Pokutta, Sebastian A1 - Gieseke, Fabian T1 - Capturing Temporal Dynamics in Large-Scale Canopy Tree Height Estimation T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/pauls25a/pauls25a.pdf VL - 267 SP - 48422 EP - 48438 ER - TY - CHAP A1 - Mundinger, Konrad A1 - Zimmer, Max A1 - Kiem, Aldo A1 - Spiegel, Christoph A1 - Pokutta, Sebastian T1 - Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/mundinger25a/mundinger25a.pdf VL - 267 SP - 45236 EP - 45255 ER - TY - CHAP A1 - Pelleriti, Nico A1 - Zimmer, Max A1 - Wirth, Elias A1 - Pokutta, Sebastian T1 - Approximating Latent Manifolds in Neural Networks via Vanishing Ideals T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/pelleriti25a/pelleriti25a.pdf VL - 267 SP - 48734 EP - 48761 ER - TY - CHAP A1 - Roux, Christophe A1 - Martínez-Rubio, David A1 - Pokutta, Sebastian T1 - Implicit Riemannian optimism with applications to min-max problems T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/roux25a/roux25a.pdf VL - 267 SP - 52139 EP - 52172 ER - TY - CHAP A1 - Turan, Berkant A1 - Asadulla, Suhrab A1 - Steinmann, David A1 - Stammer, Wolfgang A1 - Pokutta, Sebastian T1 - Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings T2 - Proceedings of the ICML Workshop on Actionable Interpretability Y1 - 2025 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Scalable Frank-Wolfe on generalized self-concordant functions via simple steps JF - SIAM Journal on Optimization Y1 - 2024 U6 - https://doi.org/10.1137/23M1616789 VL - 34 IS - 3 ER - TY - JOUR A1 - Parczyk, Olaf A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Szabó, Tibor T1 - New Ramsey multiplicity bounds and search heuristics JF - Foundations of Computational Mathematics Y1 - 2024 U6 - https://doi.org/10.1007/s10208-024-09675-6 ER - TY - CHAP A1 - Pauls, Jan A1 - Zimmer, Max A1 - Kelly, Una M A1 - Schwartz, Martin A1 - Saatchi, Sassan A1 - Ciais, Philippe A1 - Pokutta, Sebastian A1 - Brandt, Martin A1 - Gieseke, Fabian T1 - Estimating canopy height at scale T2 - Proceedings of the 41st International Conference on Machine Learning N2 - We propose a framework for global-scale canopy height estimation based on satellite data. Our model leverages advanced data preprocessing techniques, resorts to a novel loss function designed to counter geolocation inaccuracies inherent in the ground-truth height measurements, and employs data from the Shuttle Radar Topography Mission to effectively filter out erroneous labels in mountainous regions, enhancing the reliability of our predictions in those areas. A comparison between predictions and ground-truth labels yields an MAE/RMSE of 2.43 / 4.73 (meters) overall and 4.45 / 6.72 (meters) for trees taller than five meters, which depicts a substantial improvement compared to existing global-scale products. The resulting height map as well as the underlying framework will facilitate and enhance ecological analyses at a global scale, including, but not limited to, large-scale forest and biomass monitoring. Y1 - 2024 UR - https://raw.githubusercontent.com/mlresearch/v235/main/assets/pauls24a/pauls24a.pdf VL - 235 SP - 39972 EP - 39988 ER - TY - CHAP A1 - Hendrych, Deborah A1 - Besançon, Mathieu A1 - Pokutta, Sebastian T1 - Solving the optimal experiment design problem with mixed-integer convex methods T2 - 22nd International Symposium on Experimental Algorithms (SEA 2024) N2 - We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances. Y1 - 2024 U6 - https://doi.org/10.4230/LIPIcs.SEA.2024.16 VL - 301 SP - 16:1 EP - 16:22 ER - TY - CHAP A1 - Kiem, Aldo A1 - Pokutta, Sebastian A1 - Spiegel, Christoph T1 - Categorification of Flag Algebras T2 - Discrete Mathematics Days 2024 Y1 - 2024 U6 - https://doi.org/10.37536/TYSP5643 SP - 259 EP - 264 ER - TY - CHAP A1 - Kiem, Aldo A1 - Pokutta, Sebastian A1 - Spiegel, Christoph T1 - The Four-Color Ramsey Multiplicity of Triangles T2 - Discrete Mathematics Days 2024 Y1 - 2024 U6 - https://doi.org/10.37536/TYSP5643 SP - 13 EP - 18 ER - TY - JOUR A1 - Mundinger, Konrad A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Zimmer, Max T1 - Extending the Continuum of Six-Colorings JF - Geombinatorics Quarterly Y1 - 2024 VL - 34 IS - 1 SP - 20 EP - 29 ER - TY - CHAP A1 - Mundinger, Konrad A1 - Pokutta, Sebastian A1 - Spiegel, Christoph A1 - Zimmer, Max T1 - Extending the Continuum of Six-Colorings T2 - Discrete Mathematics Days 2024 Y1 - 2024 U6 - https://doi.org/10.37536/TYSP5643 SP - 178 EP - 183 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Roux, Christophe A1 - Pokutta, Sebastian T1 - Convergence and Trade-Offs in Riemannian Gradient Descent and Riemannian Proximal Point T2 - Proceedings of the 41st International Conference on Machine Learning N2 - In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different variants with several trade-offs. Crucially, we show the iterates naturally stay in a ball around an optimizer, of radius depending on the initial distance and, in some cases, on the curvature. Previous works simply assumed bounded iterates, resulting in rates that were not fully quantified. We also provide an implementable inexact proximal point algorithm and prove several new useful properties of Riemannian proximal methods: they work when positive curvature is present, the proximal operator does not move points away from any optimizer, and we quantify the smoothness of its induced Moreau envelope. Further, we explore beyond our theory with empirical tests. Y1 - 2024 UR - https://raw.githubusercontent.com/mlresearch/v235/main/assets/marti-nez-rubio24a/marti-nez-rubio24a.pdf VL - 235 SP - 34920 EP - 34948 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 - Pokutta, Sebastian T1 - The Frank-Wolfe algorithm: a short introduction JF - Jahresbericht der Deutschen Mathematiker-Vereinigung Y1 - 2024 U6 - https://doi.org/10.1365/s13291-023-00275-x VL - 126 SP - 3 EP - 35 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 The 27th 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 UR - https://proceedings.mlr.press/v238/waldchen24a/waldchen24a.pdf VL - 238 SP - 1963 EP - 1971 ER - TY - CHAP A1 - Zimmer, Max A1 - Spiegel, Christoph A1 - Pokutta, Sebastian T1 - Sparse Model Soups T2 - 12th International Conference on Learning Representations (ICLR 2024) Y1 - 2024 SN - 9781713898658 PB - Curran Associates, Inc. ER - TY - JOUR A1 - Stengl, Steven-Marian A1 - Gelß, Patrick A1 - Klus, Stefan A1 - Pokutta, Sebastian T1 - Existence and uniqueness of solutions of the Koopman--von Neumann equation on bounded domains JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2024 U6 - https://doi.org/10.1088/1751-8121/ad6f7d VL - 57 IS - 39 ER - TY - JOUR A1 - Deza, Antoine A1 - Onn, Shmuel A1 - Pokutta, Sebastian A1 - Pournin, Lionel T1 - Kissing polytopes JF - SIAM Journal on Discrete Mathematics N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1137/24M1640859 VL - 38 IS - 4 ER - TY - JOUR A1 - Kerdreux, Thomas A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Restarting Frank-Wolfe: Faster Rates under Hölderian Error Bounds JF - Journal of Optimization Theory and Applications Y1 - 2022 ER - TY - JOUR A1 - Combettes, Cyrille A1 - Pokutta, Sebastian T1 - Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm JF - Mathematical Programming A Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01735-x VL - 197 SP - 191 EP - 214 ER - TY - JOUR A1 - Vu‐Han, Tu‐Lan A1 - Sunkara, Vikram A1 - Bermudez‐Schettino, Rodrigo A1 - Schwechten, Jakob A1 - Runge, Robin A1 - Perka, Carsten A1 - Winkler, Tobias A1 - Pokutta, Sebastian A1 - Weiß, Claudia A1 - Pumberger, Matthias T1 - Feature Engineering for the Prediction of Scoliosis in 5q‐Spinal Muscular Atrophy JF - Journal of Cachexia, Sarcopenia and Muscle Y1 - 2025 U6 - https://doi.org/10.1002/jcsm.13599 VL - 16 IS - 1 SP - e13599 ER - TY - CHAP A1 - Troppens, Hannah A1 - Besançon, Mathieu A1 - Wilken, St. Elmo A1 - Pokutta, Sebastian T1 - Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks T2 - 23rd International Symposium on Experimental Algorithms (SEA 2025) Y1 - 2025 U6 - https://doi.org/10.4230/LIPIcs.SEA.2025.26 VL - 338 SP - 26:1 EP - 26:18 PB - Schloss Dagstuhl – Leibniz-Zentrum für Informatik ER - TY - CHAP A1 - Głuch, Grzegorz A1 - Turan, Berkant A1 - Nagarajan, Sai Ganesh A1 - Pokutta, Sebastian T1 - The good, the bad and the ugly: watermarks, transferable attacks and adversarial defenses T2 - 1st Workshop on GenAI Watermarking, collocated with ICLR 2025 Y1 - 2025 UR - https://openreview.net/pdf?id=rUs5ryYqZe ER - TY - CHAP A1 - Besançon, Mathieu A1 - Pokutta, Sebastian A1 - Wirth, Elias T1 - The Pivoting Framework: Frank-Wolfe Algorithms with Active Set Size Control T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/besancon25a/besancon25a.pdf VL - 258 SP - 271 EP - 279 ER - TY - CHAP A1 - Martínez-Rubio, David A1 - Roux, Christophe A1 - Criscitiello, Christopher A1 - Pokutta, Sebastian T1 - Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/martinez-rubio25a/martinez-rubio25a.pdf VL - 258 SP - 280 EP - 288 ER - TY - CHAP A1 - Sadiku, Shpresim A1 - Wagner, Moritz A1 - Pokutta, Sebastian T1 - GSE: Group-wise sparse and explainable adversarial attacks T2 - 13th International Conference on Learning Representations (ICLR 2025) Y1 - 2025 UR - https://openreview.net/pdf?id=d54fIsAbff ER - TY - JOUR A1 - Wirth, Elias A1 - Pena, Javier A1 - Pokutta, Sebastian T1 - Correction: Accelerated affine-invariant convergence rates of the Frank-Wolfe algorithm with open-loop step-sizes JF - Mathematical Programming Y1 - 2025 U6 - https://doi.org/10.1007/s10107-025-02214-3 VL - 214 SP - 941 EP - 942 ER - TY - CHAP A1 - Roux, Christophe A1 - Zimmer, Max A1 - Pokutta, Sebastian T1 - On the byzantine-resilience of distillation-based federated learning T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - 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. Y1 - 2025 UR - https://openreview.net/pdf?id=of6EuHT7de ER - TY - CHAP A1 - Sadiku, Shpresim A1 - Wagner, Moritz A1 - Nagarajan, Sai Ganesh A1 - Pokutta, Sebastian T1 - S-CFE: Simple Counterfactual Explanations T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/sadiku25a/sadiku25a.pdf VL - 258 SP - 172 EP - 180 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 - 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 - Zimmer, Max A1 - Spiegel, Christoph A1 - Pokutta, Sebastian ED - Fackeldey, K. T1 - Compression-aware training of neural networks using Frank-Wolfe T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 Y1 - 2025 U6 - https://doi.org/10.1515/9783111376776-010 SP - 137 EP - 168 PB - De Gruyter 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 - 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 - 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 - 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 - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - Braun, Gábor A1 - Guzmán, Cristóbal A1 - Pokutta, Sebastian T1 - Corrections to “Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization via Information Theory” JF - IEEE Transactions on Information Theory N2 - This note closes a gap in the proof of Theorem VI.3 from the article “Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization via Information Theory” (2017). Y1 - 2024 U6 - https://doi.org/10.1109/TIT.2024.3357200 VL - 70 IS - 7 SP - 5408 EP - 5409 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise 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 framework, the new framework 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 - 2025 U6 - https://doi.org/10.1016/j.cam.2025.116675 VL - 470 ER - TY - CHAP A1 - Lasby, Mike A1 - Zimmer, Max A1 - Pokutta, Sebastian A1 - Schultheis, Erik T1 - Compressed sparse tiles for memory-efficient unstructured and semi-structured sparsity T2 - Proceedings of the ICLR Workshop on Sparsity in LLMs Y1 - 2025 UR - https://openreview.net/forum?id=iso0KV2HVq ER - TY - CHAP A1 - Haase, Jennifer A1 - Hanel, Paul H. P. A1 - Pokutta, Sebastian T1 - S-DAT: a multilingual, GenAI-driven framework for automated divergent thinking assessment T2 - Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society (AIES) Y1 - 2025 VL - 8 SP - 1194 EP - 1205 ER - TY - JOUR A1 - Wirth, Elias A1 - Peña, Javier A1 - Pokutta, Sebastian T1 - Fast convergence of Frank-Wolfe algorithms on polytopes JF - INFORMS Journal on Mathematics of Operations Research Y1 - 2025 U6 - https://doi.org/10.1287/moor.2024.0580 ER - TY - JOUR A1 - Woodstock, Zev A1 - Pokutta, Sebastian T1 - Splitting the conditional gradient algorithm JF - SIAM Journal on Optimization Y1 - 2025 U6 - https://doi.org/10.1137/24M1638008 VL - 35 IS - 1 SP - 347 EP - 368 ER -