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arXiv · 1908.04970

Thompson Sampling with Approximate Inference

My Phan·Yasin Abbasi-Yadkori·Justin Domke
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Abstract

We study the effects of approximate inference on the performance of Thompson sampling in the $k$-armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error (in $\alpha$-divergence) can lead to poor performance (linear regret) due to under-exploration (for $\alpha<1$) or over-exploration (for $\alpha>0$) by the approximation. While for $\alpha > 0$ this is unavoidable, for $\alpha \leq 0$ the regret can be improved by adding a small amount of forced exploration even when the inference error is a large constant.

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My Phan, Yasin Abbasi-Yadkori, Justin Domke. 2019-08-14. Thompson Sampling with Approximate Inference. https://arxiv.org/abs/1908.04970

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