Thompson Sampling with Approximate Inference
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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 
-divergence) can lead to poor performance (linear regret) due to underexploration (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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