Reinforcement Learning in Decentralized Stochastic Control Systems with Partial History Sharing

TL;DR

This paper develops a decentralized reinforcement learning algorithm for multi-agent systems with partial information sharing, converting the problem into a POMDP and introducing a novel finite-state RL approach that converges rapidly, demonstrated on a broadcast channel example.

Contribution

It introduces an incremental representation method enabling finite-state RL in decentralized systems with partial history sharing, extending existing approaches to more complex settings.

Findings

The algorithm learns epsilon-team-optimal strategies in decentralized systems.

Convergence of the approximation error is exponential.

Validated through a decentralized Q-learning implementation on a multi-user broadcast channel.

Abstract

In this paper, we are interested in systems with multiple agents that wish to collaborate in order to accomplish a common task while a) agents have different information (decentralized information) and b) agents do not know the model of the system completely i.e., they may know the model partially or may not know it at all. The agents must learn the optimal strategies by interacting with their environment i.e., by decentralized Reinforcement Learning (RL). The presence of multiple agents with different information makes decentralized reinforcement learning conceptually more difficult than centralized reinforcement learning. In this paper, we develop a decentralized reinforcement learning algorithm that learns $\epsilon$-team-optimal solution for partial history sharing information structure, which encompasses a large class of decentralized control systems including delayed sharing, control sharing, mean field sharing, etc. Our approach consists of two main steps. In the first step, we convert the decentralized control system to an equivalent centralized POMDP (Partially Observable Markov Decision Process) using an existing approach called common information approach. However, the resultant POMDP requires the complete knowledge of system model. To circumvent this requirement, in the second step, we introduce a new concept called "Incrementally Expanding Representation" using which we construct a finite-state RL algorithm whose approximation error converges to zero exponentially fast. We illustrate the proposed approach and verify it numerically by obtaining a decentralized Q-learning algorithm for two-user Multi Access Broadcast Channel (MABC) which is a benchmark example for decentralized control systems.