An Information-Theoretic Analysis for Thompson Sampling with Many Actions
An Information-Theoretic Analysis for Thompson Sampling with Many Actions
复制标题
多动作汤普森采样的信息论分析
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Benjamin Van Roy
中科院分区：
文献类型：
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作者：
Shi Dong;Benjamin Van Roy
Russo和货车Roy的信息论贝叶斯后悔界限捕捉到了后悔对先验不确定性的依赖。然而，这种依赖性是通过熵来实现的，随着动作数量的增加，熵可以变得任意大。我们建立新的界限，而不是依赖于率失真的概念。除此之外，这使我们能够通过信息论的论点恢复线性强盗的接近最优的界限。我们还提供了一个边界的逻辑强盗，大大提高了最好的以前可用的，虽然这个边界取决于信息理论统计，我们只能通过计算来量化。
Information-theoretic Bayesian regret bounds of Russo and Van Roy capture the dependence of regret on prior uncertainty. However, this dependence is through entropy, which can become arbitrarily large as the number of actions increases. We establish new bounds that depend instead on a notion of rate-distortion. Among other things, this allows us to recover through information-theoretic arguments a near-optimal bound for the linear bandit. We also offer a bound for the logistic bandit that dramatically improves on the best previously available, though this bound depends on an information-theoretic statistic that we have only been able to quantify via computation.