Multi-Agent Reinforcement Learning via Double Averaging Primal-Dual Optimization (1806.00877v4)

Abstract: Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm robotics, and power grids, we study policy evaluation in MARL, where agents with jointly observed state-action pairs and private local rewards collaborate to learn the value of a given policy. In this paper, we propose a double averaging scheme, where each agent iteratively performs averaging over both space and time to incorporate neighboring gradient information and local reward information, respectively. We prove that the proposed algorithm converges to the optimal solution at a global geometric rate. In particular, such an algorithm is built upon a primal-dual reformulation of the mean squared projected BeLLMan error minimization problem, which gives rise to a decentralized convex-concave saddle-point problem. To the best of our knowledge, the proposed double averaging primal-dual optimization algorithm is the first to achieve fast finite-time convergence on decentralized convex-concave saddle-point problems.

Multi-Agent Reinforcement Learning via Double Averaging Primal-Dual Optimization

Abstract Overview

The paper addresses the challenges encountered in Multi-Agent Reinforcement Learning (MARL) due to complex agent interactions. Motivated by decentralized applications, the authors focus on policy evaluation within MARL, proposing a double averaging approach that involves iterative averaging over space and time. This method utilizes a primal-dual reformulation to solve a decentralized convex-concave saddle-point problem, achieving global geometric rate convergence. The algorithm is novel in its ability to achieve fast finite-time convergence for decentralized convex-concave saddle-point problems.

Introduction

The paper of multi-agent systems presents unique challenges distinct from single-agent reinforcement learning environments. Agents within MARL systems do not operate in isolation; rather, they interact dynamically both with their environment and with each other. Collaborative MARL with private local rewards is a pertinent area of research given its applicability in various fields such as sensor networks, swarm robotics, and power grids. This paper focuses on policy evaluation in MARL systems, where the aim is for agents to collectively maximize the global sum of local rewards. The challenge, however, arises from the need for decentralized collaboration between agents, necessitating efficient local information exchange without a central node.

Proposed Approach

The authors introduce a decentralized scheme where agents only communicate with nearby counterparts via a defined network. They propose a double averaging update mechanism combining techniques from dynamic consensus and stochastic average gradient methodologies. Through iterative processing, each agent contributes to a global consensus while maintaining local privacy and robustness against centralized point failures. The core of this approach is an incremental update of gradient tracking, both spatially and temporally, enabling agents to collectively estimate and adjust the global value function of the policy under evaluation.

Theoretical Contribution

To establish a solid mathematical framework, the proposed MARL solution is reformulated using Fenchel duality. A decentralized primal-dual optimization algorithm is developed with the double averaging scheme, assuring linear convergence rates. The authors provide rigorous analysis showcasing the geometric rate of convergence, making theirs the first algorithm to achieve such rapid convergence for decentralized saddle-point problems within MARL systems. Consequently, the solution extends beyond MARL, demonstrating applicability to broader decentralized convex-concave saddle-point problems.

Experimental Results

Empirical evaluations conducted on classic reinforcement learning datasets demonstrate the efficacy of the proposed algorithm compared to other centralized solutions such as GTD2 and SAGA. The experiments highlight the algorithm's robustness to variations in agent topology and reward structure, with convergence rates positively influenced by network connectivity and sample size.

Implications and Future Directions

The implications of this research are profound for scalable MARL applications where agent privacy and decentralization are paramount. Practical applications range from autonomous vehicle systems to collaborative robotics, highlighting the algorithm's potential to perform efficiently in environments where centralized solutions are infeasible or impractical. Future research may explore adaptations of this algorithm to other multi-agent optimization problems, possibly expanding into different types of function approximations beyond linear models or incorporating real-time dynamic changes within agent networks. As the field of AI progresses, applications requiring robust decentralized consensus will benefit greatly from these foundational advances.

In conclusion, the authors provide significant insights and contributions to the field of MARL through their innovative approach to multi-agent policy evaluation and decentralized optimization. The demonstrated theoretical guarantees, combined with practical implementation success, position this work as a benchmark for future advancements in decentralized RL systems.