Reinforcement Learning in Decentralized Stochastic Control Systems with Partial History Sharing
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 $\epsilon$teamoptimal 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 finitestate RL algorithm whose approximation error converges to zero exponentially fast. We illustrate the proposed approach and verify it numerically by obtaining a decentralized Qlearning algorithm for twouser Multi Access Broadcast Channel (MABC) which is a benchmark example for decentralized control systems.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.02051
 arXiv:
 arXiv:2012.02051
 Bibcode:
 2020arXiv201202051A
 Keywords:

 Mathematics  Optimization and Control
 EPrint:
 Proceedings of American Control Conference, 2015