$QD$-Learning: A Collaborative Distributed Strategy for Multi-Agent Reinforcement Learning Through Consensus + Innovations

TL;DR

This paper introduces a distributed $Q$-learning algorithm for multi-agent reinforcement learning that enables agents to collaboratively learn optimal policies through local processing and sparse communication, without prior knowledge of the environment.

Contribution

It proposes a novel distributed $Q$-learning method, $ ext{QD}$-learning, for multi-agent MDPs that guarantees convergence to optimal policies under weak connectivity assumptions.

Findings

Almost sure convergence to the optimal value function.

Effective collaboration through sparse communication networks.

Addresses mixed time-scale stochastic dynamics.

Abstract

The paper considers a class of multi-agent Markov decision processes (MDPs), in which the network agents respond differently (as manifested by the instantaneous one-stage random costs) to a global controlled state and the control actions of a remote controller. The paper investigates a distributed reinforcement learning setup with no prior information on the global state transition and local agent cost statistics. Specifically, with the agents' objective consisting of minimizing a network-averaged infinite horizon discounted cost, the paper proposes a distributed version of $Q$-learning, $\mathcal{QD}$-learning, in which the network agents collaborate by means of local processing and mutual information exchange over a sparse (possibly stochastic) communication network to achieve the network goal. Under the assumption that each agent is only aware of its local online cost data and the inter-agent communication network is \emph{weakly} connected, the proposed distributed scheme is almost surely (a.s.) shown to yield asymptotically the desired value function and the optimal stationary control policy at each network agent. The analytical techniques developed in the paper to address the mixed time-scale stochastic dynamics of the \emph{consensus + innovations} form, which arise as a result of the proposed interactive distributed scheme, are of independent interest.