PF-RL: Progress Field Reinforcement Learning via Goal-Conditioned Value Geometry for Vision-Language-Action Models

Most existing vision-language-action (VLA) models for robotic manipulation lack progress awareness, typically relying on hand-crafted heuristics for task termination. This limitation is particularly severe in long-horizon tasks involving cascaded sub-goals. In this work, we investigate the estimation and integration of task progress, proposing a novel model named {\textbf \vla}. Our technical contributions are twofold: (1) robust progress estimation: We pre-train a progress estimator on large-scale, unsupervised video-text robotic datasets. This estimator achieves a low prediction residual (0.07 on a scale of $[0, 1]$) in simulation and demonstrates zero-shot generalization to unseen real-world samples, and (2) differentiable progress guidance: We introduce an inverse dynamics world model that maps predicted action tokens into future latent visual states. These latents are then processed by the progress estimator; by applying a maximal progress regularization, we establish a differentiable pipeline that provides progress-piloted guidance to refine action tokens. Extensive experiments on the CALVIN and LIBERO benchmarks, alongside real-world robot deployment, consistently demonstrate substantial improvements in success rates and generalization over strong baselines.

Reinforcement learning (RL) fine-tuning has shown promise for Vision-Language-Action (VLA) models in robotic manipulation, but deployment-time visual shifts pose practical challenges. A key difficulty is that standard task rewards supervise task success, but offer limited guidance on whether a visual change is task-irrelevant or changes the behavior required for manipulation. We propose PAIR-VLA (Paired Action Invariance & Sensitivity for Visually Robust VLA), an RL fine-tuning framework to address this difficulty by adding two auxiliary objectives over paired visual variants during PPO optimization: an invariance term that reduces the discrepancy between action distributions for a task-preserving pair (e.g., different distractors), and a sensitivity objective that encourages separable action distributions for a task-altering pair (e.g., target object in a different pose). Together, these objectives turn visual variants from mere observation diversity into behavior-level guidance on policy responses during RL fine-tuning. We evaluate on ManiSkill3 across two representative VLA architectures, OpenVLA and $π_{0.5}$, under diverse out-of-distribution visual shifts including unseen distractors, texture changes, target object pose variation, viewpoint shifts, and lighting changes. Our method consistently improves over standard PPO, achieving average improvements of 16.62% on $π_{0.5}$ and 9.10% on OpenVLA. Notably, ablations further show generalization across visual shifts: invariance guidance learned from distractor and texture variants transfers to target-pose and lighting shifts, while adding sensitivity guidance on target-pose variants further improves robustness to nuisance shifts, highlighting the broader transferability of behavior-level RL guidance.

Vision-Language-Action (VLA) models such as OpenVLA, Octo, and $π_0$ have shown strong generalization by leveraging large-scale demonstrations, yet their performance is still fundamentally constrained by the quality and coverage of supervised data. Reinforcement learning (RL) provides a promising path for improving and fine-tuning VLAs through online interaction. However, conventional policy gradient methods are computationally infeasible in the context of flow-matching based models due to the intractability of the importance sampling process, which requires explicit computation of policy ratios. To overcome this limitation, we propose Flow Policy Optimization (FPO) algorithm, which reformulates importance sampling by leveraging per-sample changes in the conditional flow-matching objective. Furthermore, FPO achieves stable and scalable online reinforcement fine-tuning of the $π_0$ model by integrating structure-aware credit assignment to enhance gradient efficiency, clipped surrogate objectives to stabilize optimization, multi-step latent exploration to encourage diverse policy updates, and a Q-ensemble mechanism to provide robust value estimation. We evaluate FPO on the LIBERO benchmark and the ALOHA simulation task against supervised, preference-aligned, diffusion-based, autoregressive online RL, and $π_0$-FAST baselines, observing consistent improvements over the imitation prior and strong alternatives with stable learning under sparse rewards. In addition, ablation studies and analyses of the latent space dynamics further highlight the contributions of individual components within FPO, validating the effectiveness of the proposed computational modules and the stable convergence of the conditional flow-matching objective during online RL.