Thompson Sampling with Approximate Inference

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 -divergence) can lead to poor performance (linear regret) due to under-exploration (for <1) or over-exploration (for >0) by the approximation. While for > 0 this is unavoidable, for 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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