Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization

TL;DR

This paper introduces a novel clustering-based reinforcement learning method for multiple LQR systems, enabling personalized control policies that leverage similar system data for improved efficiency without suffering from dissimilarity bias.

Contribution

It proposes a new algorithm combining clustering and policy optimization for LQR systems, with theoretical guarantees and improved sub-optimality bounds for personalized policies.

Findings

Correct clustering with high probability under cluster separation conditions

Sub-optimality gap scales inversely with cluster size

Method incurs only mild logarithmic communication overhead

Abstract

It is known that reinforcement learning (RL) is data-hungry. To improve sample-efficiency of RL, it has been proposed that the learning algorithm utilize data from 'approximately similar' processes. However, since the process models are unknown, identifying which other processes are similar poses a challenge. In this work, we study this problem in the context of the benchmark Linear Quadratic Regulator (LQR) setting. Specifically, we consider a setting with multiple agents, each corresponding to a copy of a linear process to be controlled. The agents' local processes can be partitioned into clusters based on similarities in dynamics and tasks. Combining ideas from sequential elimination and zeroth-order policy optimization, we propose a new algorithm that performs simultaneous clustering and learning to output a personalized policy (controller) for each cluster. Under a suitable notion of cluster separation that captures differences in closed-loop performance across systems, we prove that our approach guarantees correct clustering with high probability. Furthermore, we show that the sub-optimality gap of the policy learned for each cluster scales inversely with the size of the cluster, with no additional bias, unlike in prior works on collaborative learning-based control. Our work is the first to reveal how clustering can be used in data-driven control to learn personalized policies that enjoy statistical gains from collaboration but do not suffer sub-optimality due to inclusion of data from dissimilar processes. From a distributed implementation perspective, our method is attractive as it incurs only a mild logarithmic communication overhead.