相关论文: PAPAL: A Provable PArticle-based Primal-Dual ALgor…
Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
This paper develops a distributed Nash Equilibrium seeking algorithm for heterogeneous multi-robot systems. The algorithm utilises distributed optimisation and output control to achieve the Nash equilibrium by leveraging information shared…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…
We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop.…
This work investigates a problem of simultaneous global cost minimization and Nash equilibrium seeking, which commonly exists in $N$-cluster non-cooperative games. Specifically, the agents in the same cluster collaborate to minimize a…
Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…
This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…
We propose an accelerated block proximal linear framework with adaptive momentum (ABPL$^+$) for nonconvex and nonsmooth optimization. We analyze the potential causes of the extrapolation step failing in some algorithms, and resolve this…
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to…
Reinforcement-based learning dynamics may exhibit several limitations when applied in a distributed setup. In (repeatedly-played) multi-player/action strategic-form games, and when each player applies an independent copy of the learning…
We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
Filtering algorithms are fundamental for inference on partially observed stochastic dynamic systems, since they provide access to the likelihood function and hence enable likelihood-based or Bayesian inference. A novel Poisson approximate…
This paper investigates the privacy-preserving distributed Nash equilibrium seeking problem for aggregative games. A novel differential privacy mechanism is designed by incorporating stochastic event-triggering with stochastic quantization,…
In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within…