SAVGO: Learning State-Action Value Geometry with Cosine Similarity for Continuous Control

In reinforcement learning, critics typically estimate absolute state values $V(s)$, estimating how good a particular situation is in isolation. However, it turns out that only differences in value are relevant for control. Motivated by this, we propose Relative Value Learning (RV), a framework that learns value differences directly via an antisymmetric function $Δ(s_i, s_j) = V(s_i) - V(s_j)$. We introduce a pairwise Bellman operator and prove it is a $γ$-contraction with a unique fixed point equal to the true value differences, derive well-posed $1$-step, $n$-step and $λ$-return targets and reconstruct generalized advantage estimation from pairwise differences to obtain an unbiased policy-gradient estimator (R-GAE). Beyond theoretical results, we integrate RV with PPO and achieve competitive performance on the Atari benchmark (49 ALE games) compared to standard PPO, indicating that relative value estimation is an effective alternative to absolute critics.

Reinforcement learning with verifiable rewards (RLVR) often adopts GRPO-style group-relative updates, sampling multiple rollouts per prompt to construct normalized learning signals. However, merely increasing the number of rollouts does not reliably strengthen learning: under GRPO-style group normalization, per-rollout policy-gradient features can concentrate into a low-rank, signed geometry, causing substantial cancellation during aggregation and weakening the effective update. We address this failure mode with SALT, a Subspace-Adaptive geometry pLug-in componenT that uses sample-wise gradient geometry to reweight the coefficients of group-relative updates. SALT estimates a dominant shared subspace from the mini-batch Gram geometry, decomposes group-relative coefficients into shared and residual channels, and adaptively amplifies the residual channel when signed cancellation is severe. Across diverse reasoning-oriented RLVR benchmarks and model scales, SALT improves effective update geometry and performance without modifying the reward model or the rollout sampling procedure

Reinforcement learning is a promising approach for improving the capabilities of vision-language-action (VLA) models while avoiding the heavy data requirements of imitation learning. However, its effectiveness for VLA models is often constrained by sparse supervision and the difficulty of designing informative reward signals for long-horizon manipulation. In this work, we present Feat2Go, a fine-grained value estimation framework for embodied reinforcement learning. Specifically, Feat2Go first derives a continuous progress target from a pretrained visual world model by measuring patch-level similarity to subgoal states and partitioning episodes into semantic stages with trend-based clustering. We then train an embodied value model to predict this structural progress from the current observation and task instruction, and use the predicted value to reshape terminal rewards during policy optimization. The proposed framework is compatible with existing VLA policy reinforcement learning pipelines, including PPO and GRPO, and does not rely on manual reward engineering. Extensive experiments on ManiSkill3 and RoboTwin 2.0 demonstrate that Feat2Go consistently improves the performance of existing VLA models under both single-arm and bimanual manipulation settings. More specifically, on ManiSkill3, Feat2Go improves OpenVLAOFT from 17.5% to 82.9% average out-of-distribution success while retaining 96.9% in-distribution performance. On RoboTwin 2.0, Feat2Go achieves an average success rate of 88.8% in domain-randomized task settings, outperforming prior reinforcement learning methods.