The paper proves that Thompson sampling makes at most twice the expected number of mistakes as any other policy in Bayesian bandit models. This "factor of 2" is already best possible, confirming a 2014 conjecture by Guha and Munagala. The analysis requires independent latent arm processes where each arm evolves only when played, and holds under any nonincreasing sequence of round weights, including fixed horizon and geometric discounting scenarios.
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