门控解耦组合多臂老虎机：带监督校准动作缩放与预执行门控的上下文多臂老虎机统一理论
Gated Decoupled Compositional Bandits: A Unified Theory of Contextual Bandits with Supervised-Calibrated Action Scaling and Pre-Execution Gating
AI总结：
该研究提出门控解耦组合多臂老虎机（GDCB），证明其可统一多个工业系统，核心定理可将非平稳问题转化为近似平稳问题，还推广了相关结果，配套论文已验证短期租赁动态定价实例。
AI中文摘要：
我们提出门控解耦组合多臂老虎机（Gated Decoupled Compositional Bandits, GDCB），这是一类上下文多臂老虎机算法，具备三项结构创新，共同超出了LinUCB、LinTS、HierTS、因子多臂老虎机、神经上下文多臂老虎机及RLHF的分类范畴。在GDCB系统中：（i）交付给环境的动作是名义臂（由离散或分层多臂老虎机抽取）与依赖上下文的缩放器的组合；（ii）缩放器参数在独立的监督循环中学习，而非与臂选择联合学习；（iii）每个动作均会经过预执行门控，该门控可在组合动作抵达环境前修改或否决它。我们对这类算法进行形式化，证明了四条刻画其统计行为的结构定理，并展示了六个具有工业意义的系统——短期租赁动态定价、临床药物剂量调整、信贷发放、电网需求响应、内容审核及大语言模型（LLM）工具使用智能体——均为GDCB的实例，仅在组合算子、缩放器族及门控方面存在差异。核心结果是解耦方差缩减定理：校准良好的缩放器可消除臂-奖励映射中由上下文引发的方差，将非平稳多臂老虎机问题转化为近似平稳的问题。门控诱导等价定理表明，在平稳门控下，由任意先前策略收集的历史数据均为有效的预热初始化器，无需重要性采样校正，将配套的P-HITL结果（arXiv:2606.02595）从人工批准推广至任意门控。在受监管的高风险领域，通常被视为部署阻碍的约束——批准门控、合规规则、安全屏障——实则是实现快速部署的机制，而非阻碍。配套论文已基于真实生产数据验证了实例1（短期租赁动态定价）。
英文摘要：
We introduce Gated Decoupled Compositional Bandits (GDCB), a family of contextual bandit algorithms with three structural innovations that jointly fall outside the taxonomy of LinUCB, LinTS, HierTS, factored bandits, neural contextual bandits, and RLHF. In a GDCB system: (i) the action delivered to the environment is the composition of a nominal arm, drawn by a discrete or hierarchical bandit, with a context-dependent scaler; (ii) the scaler parameter is learned in a separate supervised loop, not jointly with arm selection; and (iii) every action passes through a pre-execution gate that may modify or veto the composed action before it reaches the environment. We formalise this class of algorithms, prove four structural theorems characterising its statistical behaviour, and show that six industrially significant systems -- short-term rental dynamic pricing, clinical drug dosing, credit origination, grid demand response, content moderation, and LLM tool-use agents -- are all instances of GDCB, differing only in the composition operator, scaler family, and gate. The central result is the Decoupling Variance Reduction theorem: a well-calibrated scaler removes context-induced variance from the arm-to-reward mapping, turning a non-stationary bandit problem into an approximately stationary one. The Gate-Induced Equivalence theorem shows that under a stationary gate, historical data collected under any prior policy is a valid warm-up initialiser without importance-sampling correction, generalising the companion P-HITL result (arXiv:2606.02595) from human approval to arbitrary gates. In regulated, high-stakes domains, constraints usually treated as deployment frictions -- approval gates, compliance rules, safety shields -- are the mechanism that makes fast deployment possible, not an obstacle to it. The companion paper validates instance 1 (STR dynamic pricing) on real production data.
