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The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…

Optimization and Control · Mathematics 2021-10-11 Haoyue Wang , Haihao Lu , Rahul Mazumder

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…

Optimization and Control · Mathematics 2022-06-20 Baojian Zhou , Yifan Sun

We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction…

Numerical Analysis · Mathematics 2022-07-26 Sudhanshu Agrawal , Wonjun Lee , Samy Wu Fung , Levon Nurbekyan

The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…

Optimization and Control · Mathematics 2021-06-15 Cyrille W. Combettes , Sebastian Pokutta

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…

Machine Learning · Statistics 2018-03-22 Edward Cheung , Yuying Li

The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine…

Optimization and Control · Mathematics 2024-01-19 Liaoyuan Zeng , Yongle Zhang , Guoyin Li , Ting Kei Pong , Xiaozhou Wang

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…

Optimization and Control · Mathematics 2020-12-11 Bingcong Li , Lingda Wang , Georgios B. Giannakis , Zhizhen Zhao

We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…

Optimization and Control · Mathematics 2018-11-19 Nan Ye , Peter Bartlett

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only…

Optimization and Control · Mathematics 2018-03-21 Thomas Kerdreux , Fabian Pedregosa , Alexandre d'Aspremont

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Optimization and Control · Mathematics 2024-06-07 Wei Jiang , Sifan Yang , Wenhao Yang , Yibo Wang , Yuanyu Wan , Lijun Zhang

Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…

Analysis of PDEs · Mathematics 2018-04-25 Marco Cirant , Levon Nurbekyan

Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity…

Optimization and Control · Mathematics 2017-11-22 Liang Zhang , Gang Wang , Daniel Romero , Georgios B. Giannakis

Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the…

Machine Learning · Computer Science 2024-08-20 Ali Dadras , Sourasekhar Banerjee , Karthik Prakhya , Alp Yurtsever

We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also…

Optimization and Control · Mathematics 2019-04-01 Jean-David Benamou , Guillaume Carlier , Simone Di Marino , Luca Nenna

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…

Numerical Analysis · Mathematics 2024-04-03 Yohance A. P. Osborne , Iain Smears

This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions,…

Machine Learning · Computer Science 2024-04-30 Mohammad Pedramfar , Yididiya Y. Nadew , Christopher J. Quinn , Vaneet Aggarwal

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their…

Optimization and Control · Mathematics 2016-08-01 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic…

Optimization and Control · Mathematics 2023-02-08 Zeeshan Akhtar , Amrit Singh Bedi , Srujan Teja Thomdapu , Ketan Rajawat

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…

Optimization and Control · Mathematics 2026-02-12 Kui Ren , Nathan Soedjak , Shanyin Tong

To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…

Computer Science and Game Theory · Computer Science 2024-10-14 Jing Dong , Baoxiang Wang , Yaoliang Yu