Fixed-Confidence Guarantees for Bayesian Best-Arm Identification
This work addresses a theoretical gap in Bayesian bandit algorithms for researchers and practitioners, offering incremental improvements in computational efficiency and analysis.
The paper tackles the problem of fixed-confidence best-arm identification in Bayesian bandits by analyzing Top-Two Thompson Sampling (TTTS) and proposing a variant called T3C to reduce computational cost, providing the first sample complexity analysis for these methods with Gaussian rewards and solving an open question from Russo (2016).
We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide the first sample complexity analysis of TTTS and T3C when coupled with a very natural Bayesian stopping rule, for bandits with Gaussian rewards, solving one of the open questions raised by Russo (2016). We also provide new posterior convergence results for TTTS under two models that are commonly used in practice: bandits with Gaussian and Bernoulli rewards and conjugate priors.