Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty
<|reference_start|>Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty: This paper studies continuous-time risk-sensitive reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation with the exponential-form objective. The risk-sensitive objective arises either as the agent's risk attitude or as a distributionally robust approach against the model uncertainty. Owing to the martingale perspective in Jia and Zhou (2023) the risk-sensitive RL problem is shown to be equivalent to ensuring the martingale property of a process involving both the value function and the q-function, augmented by an additional penalty term: the quadratic variation of the value process, capturing the variability of the value-to-go along the trajectory. This characterization allows for the straightforward adaptation of existing RL algorithms developed for non-risk-sensitive scenarios to incorporate risk sensitivity by adding the realized variance of the value process. Additionally, I highlight that the conventional policy gradient representation is inadequate for risk-sensitive problems due to the nonlinear nature of quadratic variation; however, q-learning offers a solution and extends to infinite horizon settings. Finally, I prove the convergence of the proposed algorithm for Merton's investment problem and quantify the impact of temperature parameter on the behavior of the learning procedure. I also conduct simulation experiments to demonstrate how risk-sensitive RL improves the finite-sample performance in the linear-quadratic control problem.<|reference_end|>
@article{jia2024continuous-time,
    title={Continuous-time Risk-sensitive Reinforcement Learning via Quadratic
  Variation Penalty},
    author={Yanwei Jia},
    journal={arXiv preprint arXiv:2404.12598},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12598},
    primaryClass={cs.LG cs.SY eess.SY q-fin.CP q-fin.PM}
}