Operator Models for Continuous-Time Offline Reinforcement Learning
This addresses offline reinforcement learning for continuous-time systems in domains like healthcare and autonomous driving, but it appears incremental as it integrates existing statistical learning and operator theory methods.
The paper tackled the problem of limited statistical understanding of approximation errors in learning policies from offline datasets for continuous-time stochastic processes, by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm, resulting in established global convergence of the value function and finite-sample guarantees with bounds tied to system properties.
Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function and derive finite-sample guarantees with bounds tied to system properties such as smoothness and stability. Our theoretical and numerical results indicate that operator-based approaches may hold promise in solving offline reinforcement learning using continuous-time optimal control.