Related papers: Learning with Linear Function Approximations in Me…

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…

Agent-based models (ABMs) have shown promise for modelling various real world phenomena incompatible with traditional equilibrium analysis. However, a critical concern is the manual definition of behavioural rules in ABMs. Recent…

Learning-based approaches are increasingly popular for traffic control problems. However, these approaches are applied typically as black boxes with limited theoretical guarantees and interpretability. In this paper, we consider the theory…

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a…

We consider a multi-agent reinforcement learning problem where each agent seeks to maximize a shared reward while interacting with other agents, and they may or may not be able to communicate. Typically the agents do not have access to…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Recent algorithms allow decentralised agents, possibly connected via a communication network, to learn equilibria in mean-field games from a non-episodic run of the empirical system. However, these algorithms are for tabular settings: this…

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field…

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first…

Many large-scale platforms and networked control systems have a centralized decision maker interacting with a massive population of agents under strict observability constraints. Motivated by such applications, we study a cooperative Markov…

A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…

Conventional distributed approaches to coverage control may suffer from lack of convergence and poor performance, due to the fact that agents have limited information, especially in non-convex discrete environments. To address this issue,…

We study the policy evaluation problem in multi-agent reinforcement learning, modeled by a Markov decision process. In this problem, the agents operate in a common environment under a fixed control policy, working together to discover the…

In this paper, further extensions of the result of the paper "A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024" concerning a…

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Multi-agent reinforcement learning has been successfully applied to a number of challenging problems. Despite these empirical successes, theoretical understanding of different algorithms is lacking, primarily due to the curse of…

This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents…