Related papers: Last-iterate convergence of modified predictive me…
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…
Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) for saddle-point optimization have received growing attention due to their favorable last-iterate convergence. However, their behaviors for simple…
In the Lasry--Lions framework, Mean-Field Games (MFGs) model interactions among an infinite number of agents. However, existing algorithms either require strict monotonicity or only guarantee the convergence of averaged iterates, as in…
Player modeling is an important concept that has gained much attention in game research due to its utility in developing adaptive techniques to target better designs for engagement and retention. Previous work has explored modeling…
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that $UCB$, $M3$, $S$ or $Exp3$ algorithms have good behaviours on…
This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…
Feedback delays are inevitable in real-world multi-agent learning. They are known to severely degrade performance, and the convergence rate under delayed feedback is still unclear, even for bilinear games. This paper derives the rate of…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…
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…
Equilibrium computation on Riemannian manifolds provides a unifying framework for numerous problems in machine learning and data analytics. One of the simplest yet most fundamental methods is Riemannian gradient descent (RGD). While its…
Regret matching (RM) -- and its modern variants -- is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in…
We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types…
In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate…
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…
This work investigates the online machine learning problem of prediction with expert advice in an adversarial setting through numerical analysis of, and experiments with, a related partial differential equation. The problem is a repeated…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
In this paper, we propose a provably convergent and practical framework for multi-objective reinforcement learning with max-min criterion. From a game-theoretic perspective, we reformulate max-min multi-objective reinforcement learning as a…