Non-stationary Risk-sensitive Reinforcement Learning: Near-optimal Dynamic Regret, Adaptive Detection, and Separation Design

TL;DR

This paper develops algorithms for risk-sensitive reinforcement learning in non-stationary environments, providing near-optimal regret bounds and adaptive detection methods without prior knowledge of environment variation.

Contribution

It introduces restart-based algorithms with regret guarantees and a meta-algorithm for adaptive non-stationarity detection in risk-sensitive RL.

Findings

Proposed algorithms achieve near-optimal dynamic regret bounds.

Established a lower bound confirming the near-optimality of the algorithms.

Designed an adaptive algorithm that detects non-stationarity without prior knowledge.

Abstract

We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary arbitrarily over time with a budget on their cumulative variations. When this variation budget is known a prior, we propose two restart-based algorithms, namely Restart-RSMB and Restart-RSQ, and establish their dynamic regrets. Based on these results, we further present a meta-algorithm that does not require any prior knowledge of the variation budget and can adaptively detect the non-stationarity on the exponential value functions. A dynamic regret lower bound is then established for non-stationary risk-sensitive RL to certify the near-optimality of the proposed algorithms. Our results also show that the risk control and the handling of the non-stationarity can be separately designed in the algorithm if the variation budget is known a prior, while the non-stationary detection mechanism in the adaptive algorithm depends on the risk parameter. This work offers the first non-asymptotic theoretical analyses for the non-stationary risk-sensitive RL in the literature.