← 研踪 PaperTrailarXiv:2611.05227 · v1
Regret-based Characterization, Information Limits, and the Sample Complexity of Auditing Adaptive Policies
首次提交 2026-11-04 01:13
版本更新 2026-11-04 01:13
雷达观测 2026-11-04 23:39
摘要
A policy can earn its performance by where it locates on average or by reacting to information. For any Markov policy $π$ in a finite-horizon MDP, let $ν$ be its open-loop marginal, which plays $π$'s average action distribution at each step. We show that $J(π)-J(ν)$ equals $\sum_t tr Cov(Q^ν_t,π_t)$ under endogenous dynamics. Audits based on immediate costs alone can have the wrong sign. Writing the covariance as a joint-versus-product gap gives the bound $|J(π)-J(ν)|\le\sum_t span_t\sqrt{I(s_t;a_t)/2}$, with a sharp constant. Hence, an MDP's adaptivity gap is bounded by the information that its optimal policy uses. Estimating $J(π)-J(ν)$ from $π$'s own bandit-feedback logs takes $Θ(\barχ^2 \log(1/η)/δ^2)$ rounds, where $\barχ^2$ is an average $χ^2$-divergence. At the same time, deterministic non-constant policies cannot be audited at all. We also provide an importance-sampling auditor for episodic MDPs.
作者备注：13 pages
观测到的版本
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v1 · 2026-11-04 01:13 · 最新观测版本
Regret-based Characterization, Information Limits, and the Sample Complexity of Auditing Adaptive Policies
A policy can earn its performance by where it locates on average or by reacting to information. For any Markov policy $π$ in a finite-horizon MDP, let $ν$ be its open-loop marginal, which plays $π$'s average action distribution at each step. We show that $J(π)-J(ν)$ equals $\sum_t tr Cov(Q^ν_t,π_t)$ under endogenous dynamics. Audits based on immediate costs alone can have the wrong sign. Writing the covariance as a joint-versus-product gap gives the bound $|J(π)-J(ν)|\le\sum_t span_t\sqrt{I(s_t;a_t)/2}$, with a sharp constant. Hence, an MDP's adaptivity gap is bounded by the information that its optimal policy uses. Estimating $J(π)-J(ν)$ from $π$'s own bandit-feedback logs takes $Θ(\barχ^2 \log(1/η)/δ^2)$ rounds, where $\barχ^2$ is an average $χ^2$-divergence. At the same time, deterministic non-constant policies cannot be audited at all. We also provide an importance-sampling auditor for episodic MDPs.
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