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This paper introduces Vector-Symbolic Policy Gradient (VSPG), which unifies vector-symbolic architectures with standard policy gradient methods to achieve sample-efficient learning via compressed kernel memory representations. The authors provide theoretical proofs demonstrating that the update rule corresponds exactly to advantage-weighted hypervector bundling and establish robustness guarantees for action selection under noise in bipolar memories. This work advances reinforcement learning by bridging symbolic computation, log-linear policies, and kernel search within a mathematically rigorous framework.
Vector Symbolic Policy Gradient
arXiv:2608.18404v1 Announce Type: cross 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Symbolic Computation (cs.SC)
arXiv:2608.18404 [cs.LG]
(or arXiv:2608.18404v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.18404 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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