BORA: Bridging Offline Reinforcement Learning and Online Residual Adaptation for Real-World Dexterous VLA Models

Vision-Language-Action (VLA) models have emerged as a promising paradigm for grounding visual-language understanding into real-world robotic manipulation. However, dexterous manipulation remains challenging for VLA policies due to high-dimensional hand control and compounding execution errors, which makes real-world RL post-training essential for bridging the gap between visually grounded action generation and physically reliable dexterous execution. However, high-dimensional dexterous exploration often triggers temporal inconsistency, sample inefficiency and hardware risks in the real world. To address these challenges, we propose BORA, an offline-to-online RL post-training framework designed for real-world dexterous VLA models. In the offline phase, BORA constructs a critic that takes both the VLM's cognition tokens and action chunks as inputs. This design enables action-conditioned value guidance, allowing the critic to evaluate dexterous hand motions beyond visual context alone. During the subsequent online phase, BORA freezes the VLA base and introduces a lightweight, Human-in-the-Loop (HiL) chunk-wise residual adaptation mechanism to mitigate real-world execution errors and further correct the offline-learned intents within the actual physical environment. By inheriting the offline critic and employing intervention-driven rewards, BORA effectively corrects execution discrepancies and adapts to real-world physical variances while preserving the pretrained policy as a stable prior. Extensive evaluations across five complex real-world dexterous tasks demonstrate that BORA significantly outperforms pure imitation learning and traditional decoupled RL baselines, achieving a 33% absolute increase in average success rate under standard settings and up to a 43% improvement in unseen object generalization.

$π_0$-EqM: Equilibrium Matching for Closed-Loop Vision-Language-Action Control

Currently, Vision-Language-Action (VLA) models have become the most adopted paradigm for robotic manipulation for its great potential for task generalization. While most generative flow-matching action decoders for VLA control are often deployed with fixed sampling horizons, limiting state-dependent compute and temporal reuse across control cycles. We present $π_0$-EqM, which replaces the flow-matching expert in $π_0$ with an Equilibrium Matching (EqM) decoder while leaving the upstream VLA stack unchanged. Under a matched 300-step budget, $π_0$-EqM improves RoboTwin average success from 40.4% to 50.2% across 19 tasks and remains competitive on LIBERO, with its clearest gain on LIBERO-10 (87.0%). Two threshold scans reveal a task-dependent non-monotonic relation between residual and success, which we term the stationarity--executability gap. The results suggest that inference depth in iterative VLA control is part of policy design and introduce an energy-based VLA perspective that may inform future work on composable action generation across tasks and embodiments.