# Asynchronous Schemes for Stochastic and Misspecified Potential Games and Nonconvex Optimization

arXiv: https://arxiv.org/abs/1711.03963 · HTML: https://mlsanity.com/paper/1711.03963/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [Finite-Sample Analysis of Decentralized Q-Learning for Stochastic Games](https://mlsanity.com/paper/2112.07859/) (2021)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms](https://mlsanity.com/paper/2301.08015/) (2023)
- [Policy Optimization and Multi-agent Reinforcement Learning for Mean-variance Team Stochastic Games](https://mlsanity.com/paper/2503.22779/) (2025)
- [Simultaneous Learning and Optimization via Misspecified Saddle Point Problems](https://mlsanity.com/paper/2510.05241/) (2025)

## Abstract (arXiv)

The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex potential function. Our focus is on two classes of stochastic Nash games: (P1): A potential stochastic Nash game, in which each player solves a parameterized stochastic convex program; and (P2): A misspecified generalization, where the player-specific stochastic program is complicated by a parametric misspecification. In both settings, exact proximal BR solutions are generally unavailable in finite time since they necessitate solving parameterized stochastic programs. Consequently, we design two asynchronous inexact proximal BR schemes to solve the problems, where in each iteration a single player is randomly chosen to compute an inexact proximal BR solution with rivals' possibly outdated information. Yet, in the misspecified regime (P2), each player possesses an extra estimate of the misspecified parameter and updates its estimate by a projected stochastic gradient (SG) algorithm. By Since any stationary point of the potential function is a Nash equilibrium of the associated game, we believe this paper is amongst the first ones for stochastic nonconvex (but block convex) optimization problems equipped with almost-sure convergence guarantees. These statements can be extended to allow for accommodating weighted potential games and generalized potential games. Finally, we present preliminary numerics based on applying the proposed schemes to congestion control and Nash-Cournot games.