PolicyAttention: Softmax Attention Implements Policy Mirror Descent for Closed-Loop Control
Can causal softmax attention implement policy mirror descent as a repeated controller rather than a one-step algebraic identity? Negative-entropy policy mirror descent (PMD) has the statewise update $\operatorname{PMD}_η(π,Q)=\operatorname{softmax}(\logπ+ηQ)$. Building on the known Q-TD-PMD recursion, we construct one fixed causal-softmax actor--environment--one-step-critic protocol with explicit actor, routing, sampling, and normalization residuals, and propagate them to the policy actually returned. The construction states the finite-logit/full-support domain, the external tokenization and sampling boundary, and the mean-zero LayerNorm carrier conditions required by the normalized compi...
| Authors | Yuhe Sui, Yingzhi Tang, Shufang Chen |
|---|---|
| Primary category | cs.LG |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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