Large Deviations Analysis For Regret Minimizing Stochastic Approximation Algorithms

TL;DR

This paper analyzes the probability of rare deviations in a multi-agent regret minimization algorithm using large deviations theory, providing insights into its convergence behavior.

Contribution

It introduces a large deviations framework for analyzing regret minimizing stochastic approximation algorithms with multi-agent communication.

Findings

Exponential decay rate towards stable point derived

Large deviations principles applied to multi-agent regret algorithms

Characterization of rare event probabilities in convergence analysis

Abstract

Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple agents that communicate over a graph to coordinate their decisions. We derive an exponential decay rate towards the algorithm's stable point using large deviations theory. Our analysis leverages the variational representation of the Laplace functionals and weak convergence methods to characterize the exponential decay rate.