arXiv research

New algorithm solves non-convex, non-differentiable min-max games.

The paper explains how simple methods can converge to optimal solutions in complex neural games.

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…

New algorithm solves min-max optimization problems in a decentralized manner.

Survey of advances in non-convex min-max optimization for applications.

OMWU shows last iterate convergence in convex-concave games.

Adaptive momentum method solves non-convex min-max problems.

Study proves value of non-Markovian games with partial, asymmetric info.

Study introduces statistical mechanics for min-max problems.

Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Asce…

A new method solves bilevel optimization problems in competitive Markov games.

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be computed efficiently. In this paper, we study the problem in the non-convex reg…

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they…

New framework crafts adversarial examples for neural networks.

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower boun…

New algorithms reduce variance in solving complex mathematical problems.

Certified algorithms optimize functions with varying costs, providing error bounds.

Reward suffices for convex MDPs, expanding RL to new problems.

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…

Omega method mitigates noise in stochastic game optimization.

Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vani…

Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.

New neural approach for estimating SEMs with provable convergence.

This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpret…

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…

Paper finds algorithms with both low regret and high exploitation.

New algorithms solve nonconvex-nonconcave minimax optimization problems.

Study shows strong min-max principle for phase transitions.

Equity-Transformer solves NP-hard min-max routing problems efficiently.

Reinforcement learning algorithms, though successful, tend to over-fit to training environments hampering their application to the real-world. This paper proposes $\text{W}\text{R}^{2}\text{L}$ -- a robust reinforcement learning algorithm with significant robust performance on low and high-dimensional control tasks. Ou…

This paper shows how to learn variational inequalities fast with strong monotonicity.

Upper bound for Morse index of min-max varifolds.

Localized min-max method proves minimal hypersurface existence.

The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.

Paper proves finiteness and Morse index estimates for equivariant min-max hypersurfaces.

New proof of Smale conjecture for RP^3 and lens spaces using min-max theory.

Paper improves Morse index bound for hypersurfaces.

New methods solve min-max problems on manifolds using Riemannian Hamiltonians.

Bound on equivariant index for min-max surfaces.

We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each…

We reformulate LIPs as min-max problems for easier solution.

Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.

The paper bounds the min-max width of embedded circles on spheres and manifolds.