Vector-Symbolic Policy Gradient (VSPG), a discrete-action actor that represents each action by a unit-norm hypervector and scores it by similarity to the encoded state, connects VSA action memories, log-linear policy gradients, and kernel policy search while providing a quantitative robustness guarantee.
Abstract
We answer this question with Vector-Symbolic Policy Gradient (VSPG), a discrete-action actor that represents each action by a unit-norm hypervector and scores it by similarity to the encoded state. Under the standard softmax policy-gradient surrogate, we prove that its update is exactly advantage-weighted hypervector bundling followed by normalization, and therefore supports standard advantage estimators. We further show that each trained action hypervector is a fixed-size compressed kernel memory, storing an advantage-weighted kernel expansion over visited states and transferring evidence according to the encoder-induced similarity. This provides a concrete mechanism that can support sample-efficient learning without increasing inference-time memory. Finally, for bipolar action memories, we prove that greedy action selection is stable under random bit flips, with failure probability decaying exponentially in the hypervector dimension. VSPG thus connects VSA action memories, log-linear policy gradients, and kernel policy search while providing a quantitative robustness guarantee.
It is shown that score-conditioned In-Context Learning (ICL) admits a structural correspondence to policy gradient optimization, and an exact upper bound on the distribution shift induced by a bounded attention update is derived, yielding a trust-region-like analogy to KL-constrained policy optimization.
Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.
Zhijian Zhou, Long Li, Xuan Zhang et al.· 1 citation· ⚡1
Goal-conditioned reinforcement learning hinges on how the goal is encoded. Contrastive, metric, temporal-distance, and information-theoretic encoders differ in objective. They still share one trait. None of them sees the current state. Such a state-independent embedding cannot mark which part of the goal still needs action. The policy must then recover that cue by inverting both encoders. We propose DAGR. It refines the static embedding of any late-fusion encoder into a state-conditioned one through multi-scale gated cross-attention. A near-identity gated residual preserves the base representation. Difference-aware Goal Cross-Attention then biases the attention scores using a per-token state-goal discrepancy map. On OGBench, DAGR improves navigation. Our ablations trace the gain to the gated residual, not to the difference bias that names the method. On manipulation and puzzle tasks it matches or falls below the base. DAGR is a structured refinement, not a universal improvement.
Xing Lei, Wenyan Yang, Xuetao Zhang et al.· 0 citations
Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.
Haoze Wu, Chuqiao Kuang, Tianyi Zhuang et al.· 0 citations
This work introduces ORCAID, a novel method for extracting interpretable rule-based policies from RL agents operating in mixed continuous-discrete environments with continuous action spaces, with an efficient oblique decision tree training algorithm that partitions the state space by hyperplanes and fits local linear models.
Ignacio D. Lopez-Miguel, E. Bartocci, Thomas Eiter et al.· 0 citations
