q-Learning in Continuous Time

• URL: http://arxiv.org/abs/2207.00713v3
• Date: Mon, 24 Apr 2023 00:18:09 GMT
• Title: q-Learning in Continuous Time
• Authors: Yanwei Jia and Xun Yu Zhou
• Abstract summary: We study the continuous-time counterpart of Q-learning for reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation. We develop a q-learning" theory around the q-function that is independent of time discretization. We devise different actor-critic algorithms for solving underlying problems.
• Score: 1.4213973379473654
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the continuous-time counterpart of Q-learning for reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation introduced by Wang et al. (2020). As the conventional (big) Q-function collapses in continuous time, we consider its first-order approximation and coin the term ``(little) q-function". This function is related to the instantaneous advantage rate function as well as the Hamiltonian. We develop a ``q-learning" theory around the q-function that is independent of time discretization. Given a stochastic policy, we jointly characterize the associated q-function and value function by martingale conditions of certain stochastic processes, in both on-policy and off-policy settings. We then apply the theory to devise different actor-critic algorithms for solving underlying RL problems, depending on whether or not the density function of the Gibbs measure generated from the q-function can be computed explicitly. One of our algorithms interprets the well-known Q-learning algorithm SARSA, and another recovers a policy gradient (PG) based continuous-time algorithm proposed in Jia and Zhou (2022b). Finally, we conduct simulation experiments to compare the performance of our algorithms with those of PG-based algorithms in Jia and Zhou (2022b) and time-discretized conventional Q-learning algorithms.

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