Related papers: Newton Optimization on Helmholtz Decomposition for…

We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust…

Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

We analyze the influence of multiplayer interactions and network adaptation on the stability of equilibrium points in evolutionary games. We consider the Snowdrift game with both two-player and three-player interactions on simplicial…

In this paper, we propose a passivity-based methodology for analysis and design of reinforcement learning in multi-agent finite games. Starting from a known exponentially-discounted reinforcement learning scheme, we show that convergence to…

High-order optimization methods, including Newton's method and its variants as well as alternating minimization methods, dominate the optimization algorithms for tensor decompositions and tensor networks. These tensor methods are used for…

In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…

We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…

Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…

This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…

In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…

We study sequential decision-making when the agent's internal model class is misspecified. Within the infinite-horizon Berk-Nash framework, stable behavior arises as a fixed point: the agent acts optimally relative to a subjective model,…

In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…

Finding Nash equilibria in two-player zero-sum imperfect-information games remains a central challenge in multi-agent reinforcement learning. Recent multi-round regularization methods offer a promising direction, yet existing approaches…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…

This paper proposes a novel federated algorithm that leverages momentum-based variance reduction with adaptive learning to address non-convex settings across heterogeneous data. We intend to minimize communication and computation overhead,…

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…