Near-Optimal Policy Optimization Algorithm for Computing Correlated Equilibrium in General-Sum Markov Games

Core Concepts

This paper proposes a near-optimal policy optimization algorithm that converges to a correlated equilibrium in general-sum Markov games at a rate of O((log T)^2/T), significantly improving upon the previous best rates.

Abstract

The paper studies policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov games. Previous results achieved a convergence rate of O(T^-1/2) to a correlated equilibrium and O(T^-3/4) to the weaker notion of coarse correlated equilibrium. The authors present an uncoupled policy optimization algorithm that attains a near-optimal O((log T)^2/T) convergence rate for computing a correlated equilibrium. The algorithm combines two key elements: (i) smooth value updates and (ii) the optimistic-follow-the-regularized-leader algorithm with the log barrier regularizer. The analysis shows that the output policy of the algorithm is an approximate correlated equilibrium as long as each player has low per-state weighted swap regret. The authors prove that their algorithm achieves the desired per-state regret bound, leading to the near-optimal convergence rate for correlated equilibrium. This result significantly improves upon the previous best rates for finding correlated equilibrium and coarse correlated equilibrium in general-sum Markov games.

Stats

The previous best convergence rate for finding correlated equilibrium was O(T^-1/2). The previous best convergence rate for finding coarse correlated equilibrium was O(T^-3/4). The proposed algorithm achieves a near-optimal convergence rate of O((log T)^2/T) for computing correlated equilibrium.

Quotes

"Previous results achieve ˜O(T −1/2) convergence rate to a correlated equilibrium and an accelerated ˜O(T −3/4) convergence rate to the weaker notion of coarse correlated equilibrium." "In this work, we close this gap by proposing an uncoupled policy optimization algorithm that converges to a CE (thus also to the weaker notion of CCE) at a near-optimal rate of log2(T)/T = ˜O(T −1), significantly improving existing results."

Key Insights Distilled From

Near-Optimal Policy Optimization for Correlated Equilibrium in General-Sum Markov Games

by Yang Cai,Hai... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2401.15240.pdf

Deeper Inquiries

How can the proposed algorithm be extended to handle partial observability or imperfect information in the Markov games

To extend the proposed algorithm to handle partial observability or imperfect information in Markov games, we can incorporate techniques from reinforcement learning, such as deep reinforcement learning or partially observable Markov decision processes (POMDPs). By using neural networks to approximate the value functions or policies, the algorithm can learn to make decisions based on limited information or uncertain observations. Additionally, techniques like recurrent neural networks or attention mechanisms can help capture temporal dependencies and handle partial observability more effectively. By integrating these methods into the algorithm, we can enhance its ability to deal with complex and uncertain environments.

Can the techniques used in this work be applied to other equilibrium concepts beyond correlated equilibrium, such as Nash equilibrium or Stackelberg equilibrium

The techniques used in this work can be applied to other equilibrium concepts beyond correlated equilibrium, such as Nash equilibrium or Stackelberg equilibrium. For Nash equilibrium, the algorithm can be adapted to optimize individual player strategies to reach a stable outcome where no player has an incentive to unilaterally deviate. By adjusting the objective function and constraints, the algorithm can converge to a Nash equilibrium in various game settings. Similarly, for Stackelberg equilibrium, where one player acts as a leader and others as followers, the algorithm can be modified to model the hierarchical decision-making process and optimize strategies accordingly. By incorporating the specific constraints and dynamics of each equilibrium concept, the algorithm can be tailored to compute different types of equilibria in multi-agent systems.

What are the potential applications of the near-optimal correlated equilibrium computation in real-world multi-agent systems

The near-optimal correlated equilibrium computation in real-world multi-agent systems has several potential applications across various domains. One application is in autonomous driving, where multiple self-driving vehicles need to coordinate their actions to ensure safe and efficient traffic flow. By computing correlated equilibria, the algorithm can help vehicles make decisions that consider the overall system's welfare, leading to smoother traffic patterns and reduced congestion. In online auctions and marketplaces, the algorithm can be used to optimize bidding strategies of multiple agents to reach equilibrium states that maximize overall utility. Additionally, in cooperative robotics and multi-agent systems, the algorithm can facilitate collaboration among robots or agents to achieve common goals while maintaining fairness and efficiency. Overall, the near-optimal correlated equilibrium computation can enhance decision-making processes in complex multi-agent systems, leading to more effective and coordinated outcomes.