Non-stationary Risk-Sensitive Reinforcement Learning: Near-Optimal Dynamic Regret, Adaptive Detection, and Separation Design
Yuhao Ding, Ming Jin, Javad Lavaei
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.
BibTeX
@article{Ding_Jin_Lavaei_2023, title={Non-stationary Risk-Sensitive Reinforcement Learning: Near-Optimal Dynamic Regret, Adaptive Detection, and Separation Design}, volume={37}, url={https://ojs.aaai.org/index.php/AAAI/article/view/25901}, DOI={10.1609/aaai.v37i6.25901}, abstractNote={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.}, number={6}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Ding, Yuhao and Jin, Ming and Lavaei, Javad}, year={2023}, month={Jun.}, pages={7405-7413} }