面向不确定基线的保守型多臂赌博机：考虑储备的对比证书
Reserve-Aware Contrast Certificates for Conservative Bandits with Uncertain Baselines
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中文总结 AI 辅助
针对基线不确定的保守型赌博机问题，提出Reserve-C4B方法，利用共享置信集和储备账本减少重复计费，并通过前缀刷新实现动态重认证，显著降低基线回退。
中文摘要 AI 辅助
保守型多臂赌博机必须在不超过规定性能预算的前提下改进现有策略。当基线不确定时，分别界定候选奖励和基线奖励可能会因共享的估计误差而重复计费。我们围绕基线相对对比本身开发了Reserve-C4B。共享置信集为这一可避免的惩罚提供了精确表达式，并在每个固定历史下提供了更严格的可行性检验。储备账本将统计证据与允许的性能赤字分开；前缀刷新扩展在当前置信集下重新认证累积决策，而不丢弃先前认证的信用。对于线性奖励，自归一化置信集在时间上和自适应生成的候选上提供同时有效性，所得策略以高概率满足条件均值性能约束。可复现的实验隔离了证书耦合、前缀刷新和历史信息，显示出基线回退的大幅减少，同时揭示了冻结证书的局限性。
英文摘要
Conservative bandits must improve an incumbent policy without exhausting a prescribed performance budget. When the incumbent is uncertain, separately bounding candidate and baseline rewards can charge twice for shared estimation error. We develop Reserve-C4B around the baseline-relative contrast itself. A shared confidence set yields an exact expression for this avoidable penalty and a tighter admissibility test at every fixed history. A reserve ledger separates statistical evidence from permitted performance deficit; a prefix-refresh extension recertifies accumulated decisions under the current confidence set without discarding previously certified credit. For linear rewards, self-normalized confidence sets provide simultaneous validity over time and adaptively generated candidates, and the resulting policy satisfies a conditional-mean performance constraint with high probability. Reproducible experiments isolate certificate coupling, prefix refresh, and historical information, showing large reductions in baseline fallback while exposing the limitations of frozen certificates.
