Distributed Generalized Nash Equilibria Learning for Online Stochastic Aggregative Games

TL;DR

This paper proposes a distributed online stochastic algorithm for learning generalized Nash equilibria in complex, time-varying aggregative games with local constraints, providing convergence guarantees and high-probability bounds.

Contribution

It introduces a novel push-sum and primal-dual based distributed algorithm for online stochastic games with partial information and constraints, with rigorous convergence analysis.

Findings

High probability bounds on regret and constraint violation.

Almost sure convergence to variational GNE in strongly monotone games.

Sublinear convergence of time-averaged sequences.

Abstract

This paper investigates online stochastic aggregative games subject to local set constraints and time-varying coupled inequality constraints, where each player possesses a time-varying expectation-valued cost function relying on not only its own decision variable but also an aggregation of all the players' variables. Each player can only access its local individual cost function and constraints, necessitating partial information exchanges with neighboring players through time-varying unbalanced networks. Additionally, local cost functions and constraint functions are not prior knowledge and only revealed gradually. To learn generalized Nash equilibria of such games, a novel distributed online stochastic algorithm is devised based on push-sum and primal-dual strategies. Through rigorous analysis, high probability bounds on the regret and constraint violation are provided by appropriately selecting decreasing stepsizes. Moreover, for a time-invariant stochastic strongly monotone game, it is shown that the generated sequence by the designed algorithm converges to its variational generalized Nash equilibrium (GNE) almost surely, and the time-averaged sequence converges sublinearly with high probability. Finally, the derived theoretical results are illustrated by numerical simulations.