Reinforcement learning method improves control near boundaries in continuous spaces
Boundary-aware Reinforcement Learning for Hypercube State Spaces via Deterministic Policy Gradient
Machine Learning
Summary
Controlling systems where changes happen continuously and states are confined within limits can be tricky because standard methods may ignore boundary behaviors. The authors develop a new reinforcement learning approach that carefully treats boundaries in such spaces, using mathematical tools involving reflected stochastic processes. Their method helps ensure policies respect these boundaries and improves learning stability, demonstrated in control problems like managing water reservoirs. This research bridges theory and practical algorithms for continuous control with boundaries.
What this means in practice
- •For industrial control engineers: Improve continuous control algorithms in systems where state constraints create boundary reflections, such as reservoir or chemical process control.
- •For robotics developers: Enhance robot policy learning when operating in confined state spaces requiring explicit boundary behavior handling.
Authors
Lijun Bo, Yijie Huang, Chenhao Lu
Abstract
We develop a continuous-time deterministic policy gradient framework for reinforcement learning with reflected state dynamics, where the state process is governed by a controlled reflected stochastic differential equation on a hypercube. Under suitable regularity assumptions, we establish the connection between the value function and the Neumann Bellman equation, introduce an advantage-rate function that yields a deterministic policy gradient formula, and prove the martingale characterization theorem. Motivated by these theoretical results, we propose a continuous-time deep deterministic policy gradient algorithm for reflected stochastic systems, in which the Neumann boundary condition is imposed via either soft penalization or hard architectural constraint. We further quantify the discrepancy between the ideal continuous-time dynamics and the discretely sampled exploratory dynamics executed in practice, showing that the error decays as the time grid is refined and exploration noise vanishes. Our experiments on reservoir control problems illustrate the effectiveness of the RL framework, highlighting that boundary-aware methods substantially reduce Neumann boundary residuals and enhance learning stability.