Thompson Sampling Proven to Make at Most 2x Mistakes in Bandit Models

Mark Sellke and Gregory Valiant have published a paper proving that Thompson sampling—a widely used algorithm for decision-making under uncertainty—makes at most twice the expected number of mistakes (selecting a suboptimal arm) compared to any other policy in Bayesian bandit models. This tight bound, with factor 2 being the best possible, confirms a 2014 conjecture by Guha and Munagala. The proof holds for any nonincreasing sequence of round weights, including fixed horizon and geometric discounting, and requires only that arms are independent and evolve only when played.

For practitioners, this means Thompson sampling now carries a strong theoretical guarantee: no matter how you weight time, it can't be more than twice as bad as the optimal strategy. This is especially relevant for A/B testing platforms, recommendation engines, and any system facing explore-exploit tradeoffs. The result validates the empirical popularity of Thompson sampling and offers confidence in its use without complex tuning. As reinforcement learning and bandit algorithms grow in industry, such crisp guarantees help engineers deploy with assurance.