Reinforcement Learning via Value Gradient Flow

Haoran Xu, Kaiwen Hu, Somayeh Sojoudi, Amy Zhang

Keywords: rl with generative models, offline rl, llm rl, flow matching, optimal transport

TL;DR: A new paradigm that reframes behavior-regularized RL as limited-budget optimal transport from the behavior distribution to the Boltzmann value distribution. It scales to large generative models and enables adaptive test-time scaling.

Abstract: We study behavior-regularized reinforcement learning (RL), where regularization toward a reference distribution (the dataset in offline RL or the base model in LLM RL finetuning) is essential to prevent value over-optimization caused by erroneous out-of-distribution extrapolation. Existing methods either rely on reparameterized policy gradient, which are difficult to scale to large generative models, or on reject sampling, which can be overly conservative when attempting to move beyond the behavior support. In this paper, we propose Value Gradient Flow (VGF), a scalable new paradigm for behavior-regularized RL. VGF casts behavior-regularized RL as an optimal transport problem that maps the reference distribution to the value-induced optimal policy distribution. We solve this transport problem via discrete gradient flow, where value gradients guide particles initialized from the reference distribution. Our analysis shows that VGF imposes regularization implicitly by controlling the transport budget. VGF eliminates explicit policy parameterization while remaining expressive and flexible, this enables adaptive test-time scaling by adjusting the transport budget. Extensive experiments demonstrate that VGF significantly outperforms prior methods, achieving state-of-the-art results on offline RL benchmarks (D4RL, OGBench) and LLM RL tasks.

Primary Area: reinforcement learning

Submission Number: 691