Fast, Precise Thompson Sampling for Bayesian Optimization
This work addresses a specific bottleneck in Bayesian optimization for researchers and practitioners, offering an incremental improvement over prior methods.
The paper tackles the underperformance of Thompson sampling in Bayesian optimization by introducing the Stagger Thompson Sampler (STS), which more precisely locates the maximizer with less computation time and outperforms existing methods like TS, PSS, and others in numerical experiments across various dimensions.
Thompson sampling (TS) has optimal regret and excellent empirical performance in multi-armed bandit problems. Yet, in Bayesian optimization, TS underperforms popular acquisition functions (e.g., EI, UCB). TS samples arms according to the probability that they are optimal. A recent algorithm, P-Star Sampler (PSS), performs such a sampling via Hit-and-Run. We present an improved version, Stagger Thompson Sampler (STS). STS more precisely locates the maximizer than does TS using less computation time. We demonstrate that STS outperforms TS, PSS, and other acquisition methods in numerical experiments of optimizations of several test functions across a broad range of dimension. Additionally, since PSS was originally presented not as a standalone acquisition method but as an input to a batching algorithm called Minimal Terminal Variance (MTV), we also demon-strate that STS matches PSS performance when used as the input to MTV.