New Regret Bounds Established for Thompson Sampling in Bayesian Optimization
Researchers have derived new regret bounds for Gaussian process Thompson sampling (GP-TS), a widely-used Bayesian optimization method, addressing gaps in existing theoretical analyses. The work establishes both lower and upper bounds on regret under different conditions, including high-probability bounds and improved cumulative regret bounds. These theoretical results advance understanding of GP-TS performance guarantees, which is important for validating and improving optimization algorithms used in machine learning applications.
A new theoretical analysis of Gaussian process Thompson sampling (GP-TS) provides several regret bounds that extend beyond previous work limited primarily to expected regret analysis. The paper establishes a regret lower bound showing that GP-TS suffers polynomial dependence on 1/δ with probability δ, an upper bound on the second moment of cumulative regret, expected lenient regret upper bounds, and an improved cumulative regret upper bound on the time horizon T. The authors also provide relaxed conditions for obtaining improved regret bounds compared to recent analyses of the related GP-UCB method. This work fills theoretical gaps regarding whether recent improvements in GP-UCB analysis could apply to the more commonly-used GP-TS approach, contributing to the formal understanding of this optimization algorithm's convergence properties.
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- arXiv cs.LGCenter
On Regret Bounds of Thompson Sampling for Bayesian Optimization
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