Q-Learning with Scalar Adjoint Matching

2026-10-07

AI Summary

This study addresses the prohibitive computational cost of adjoint matching in flow policy offline reinforcement learning fine-tuning, which stems from stepwise vector-Jacobian products. To overcome this bottleneck, we propose SQAM, a method that exploits the diagonal concentration property of the pre-trained velocity Jacobian to derive a closed-form scalar adjoint. This formulation reduces the complex vector adjoint to a time-dependent scalar form, thereby eliminating the overhead of stepwise backpropagation. Furthermore, SQAM incorporates a value penalty mechanism to facilitate efficient policy optimization. Empirically, our approach surpasses the strongest baseline by 18–35% in success rate on challenging OGBench tasks and significantly outperforms supervised fine-tuning when deployed on a real-world bimanual robot.

Abstract

Flow policies capture rich and diverse action distributions, and fine-tuning them with off-policy RL to improve beyond the demonstrations has drawn growing interest. However, fine-tuning a flow policy against a learned value function is not trivial, because the policy generates its action over many flow steps. Adjoint matching offers a principled way to update the flow model itself by propagating value information from the final action back to each flow step, but it requires a vector--Jacobian product through the policy at every step, a cost that grows with the number of flow steps and the policy size. We observe that the batch-averaged velocity Jacobian of pretrained flow policies concentrates on its diagonal. Motivated by this finding, we derive a closed-form scalar adjoint that scales the value gradient at the final action by the flow time, eliminating the per-step vector--Jacobian products. We further find that controlling the critic's value at policy-generated actions is particularly important under the scalar adjoint. Based on these findings, we propose Q-learning with Scalar Adjoint Matching (SQAM), which combines the scalar adjoint with a value penalty at those actions. SQAM's gains concentrate on the four hardest OGBench domains, where its success rate exceeds that of the strongest baseline in each domain by 18 to 35 percentage points. To test whether SQAM extends to large pretrained policies, we also fine-tune a vision-language-action policy on a real bimanual robot. SQAM improves over supervised fine-tuning on all three tasks.

Problem

• flow policy
• off-policy reinforcement learning
• fine-tuning
• adjoint matching
• vector-Jacobian product

Innovation

• Scalar Adjoint Matching
• Flow Policy
• Off-policy Reinforcement Learning
• Jacobian Diagonal Concentration
• Vision-Language-Action Fine-tuning