On the Suboptimality of Thompson Sampling in High Dimensions
This reveals a critical limitation of TS for high-dimensional bandit problems, which is incremental as it identifies a specific failure case rather than proposing a new solution.
The paper demonstrates that Thompson Sampling (TS) suffers from suboptimal regret scaling exponentially in ambient dimensions for combinatorial semi-bandits, with theoretical and numerical evidence showing poor performance in high-dimensional scenarios.
In this paper we consider Thompson Sampling (TS) for combinatorial semi-bandits. We demonstrate that, perhaps surprisingly, TS is sub-optimal for this problem in the sense that its regret scales exponentially in the ambient dimension, and its minimax regret scales almost linearly. This phenomenon occurs under a wide variety of assumptions including both non-linear and linear reward functions, with Bernoulli distributed rewards and uniform priors. We also show that including a fixed amount of forced exploration to TS does not alleviate the problem. We complement our theoretical results with numerical results and show that in practice TS indeed can perform very poorly in some high dimensional situations.