Deep Q-learning: a robust control approach

TL;DR

This paper reinterprets deep Q-learning through a control theory lens, using robust control techniques to analyze and improve its learning stability and convergence without relying on traditional RL heuristics.

Contribution

It introduces a control-oriented framework for deep Q-learning, employing robust controllers like H2 and Hinf to enhance stability and convergence, replacing target networks and replay buffers.

Findings

Hinf controllers slightly outperform Double deep Q-learning in simulations.

The control-based approach offers greater transparency and theoretical grounding.

Learning stability can be improved using robust control techniques.

Abstract

In this paper, we place deep Q-learning into a control-oriented perspective and study its learning dynamics with well-established techniques from robust control. We formulate an uncertain linear time-invariant model by means of the neural tangent kernel to describe learning. We show the instability of learning and analyze the agent's behavior in frequency-domain. Then, we ensure convergence via robust controllers acting as dynamical rewards in the loss function. We synthesize three controllers: state-feedback gain scheduling H2, dynamic Hinf, and constant gain Hinf controllers. Setting up the learning agent with a control-oriented tuning methodology is more transparent and has well-established literature compared to the heuristics in reinforcement learning. In addition, our approach does not use a target network and randomized replay memory. The role of the target network is overtaken by the control input, which also exploits the temporal dependency of samples (opposed to a randomized memory buffer). Numerical simulations in different OpenAI Gym environments suggest that the Hinf controlled learning performs slightly better than Double deep Q-learning.