Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Control

• URL: http://arxiv.org/abs/2510.17122v1
• Date: Mon, 20 Oct 2025 03:30:32 GMT
• Title: Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Control
• Authors: Chengxiu Hua, Jiawen Gu, Yushun Tang,
• Abstract summary: We introduce a novel method for continuous-time control, where differential equations govern state-action dynamics.<n>Our key contribution is the characterization of continuous-time Q-functions via a martingale condition.<n> Notably, our method addresses a long-standing challenge in continuous-time RL: preserving the action-evaluation capability of Q-functions without relying on time discretization.
• Score: 5.975906953272315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement learning (RL) has achieved significant success across a wide range of domains, however, most existing methods are formulated in discrete time. In this work, we introduce a novel RL method for continuous-time control, where stochastic differential equations govern state-action dynamics. Departing from traditional value function-based approaches, our key contribution is the characterization of continuous-time Q-functions via a martingale condition and the linking of diffusion policy scores to the action gradient of a learned continuous Q-function by the dynamic programming principle. This insight motivates Continuous Q-Score Matching (CQSM), a score-based policy improvement algorithm. Notably, our method addresses a long-standing challenge in continuous-time RL: preserving the action-evaluation capability of Q-functions without relying on time discretization. We further provide theoretical closed-form solutions for linear-quadratic (LQ) control problems within our framework. Numerical results in simulated environments demonstrate the effectiveness of our proposed method and compare it to popular baselines.

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