Q-Learning with Scalar Adjoint Matching
SQAM fine-tunes flow policies with a scalar adjoint, beating baselines by 18 to 35 points on hard OGBench tasks.
SQAM replaces per-step vector-Jacobian products in adjoint matching with a closed-form scalar adjoint that scales the final-action value gradient by flow time, motivated by diagonal concentration of pretrained flow-policy velocity Jacobians. A value penalty keeps the critic controlled at policy-generated actions. On the four hardest OGBench domains, success exceeds the strongest baseline by 18 to 35 percentage points. Fine-tuning a vision-language-action policy on a real bimanual robot improves all three tasks over supervised fine-tuning.
- Scalar adjoint removes per-step vector-Jacobian products through the policy.
- A value penalty constrains the critic at policy-generated actions.
- Success rises 18 to 35 points on the four hardest OGBench domains.
- Real bimanual vision-language-action fine-tuning beats supervised fine-tuning.
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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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2610.10437