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• W1528131421 abstract "The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(sqrt{T/p})$ and $O(sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge." @default.
• W1528131421 created "2016-06-24" @default.
• W1528131421 creator A5030089269 @default.
• W1528131421 creator A5054850777 @default.
• W1528131421 date "2015-06-10" @default.
• W1528131421 modified "2023-09-26" @default.
• W1528131421 title "On the Prior Sensitivity of Thompson Sampling" @default.
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• W1528131421 doi "https://doi.org/10.48550/arxiv.1506.03378" @default.
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