Reinforcement Learning via Value Gradient Flow

TL;DR

This paper introduces Value Gradient Flow (VGF), a scalable reinforcement learning method that uses optimal transport to regularize behavior, outperforming prior approaches on offline RL and LLM tasks.

Contribution

VGF reformulates behavior-regularized RL as an optimal transport problem solved via gradient flow, eliminating explicit policy parameterization and enabling adaptive scaling.

Findings

VGF achieves state-of-the-art results on offline RL benchmarks.

VGF outperforms existing methods on LLM RL tasks.

VGF provides a scalable and flexible framework for behavior-regularized RL.

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. Code and runs can be found at https://ryanxhr.github.io/vgf.