notesum.ai

Published at December 3

stat.ML

cs.AI

cs.LG

econ.EM

math.PR

Released Date: December 3, 2024

Authors: Pengjie Zhou¹, Haoyu Wei², Huiming Zhang¹

Aff.: ¹Institute of Artificial Intelligence, Beihang University, Beijing, China; ²Department of Economics, University of California, San Diego

Aspect	GP-UCB	GP-TS
Acquisition Function Definition	Combines the posterior mean and variance with a confidence parameter to form an upper confidence bound.	Directly uses a function sampled from the GP posterior as the acquisition function.
Exploration vs. Exploitation	Explicitly balances exploration and exploitation through the parameter $\beta_{t}$ , which scales the influence of the uncertainty term $\sigma_{t-1}(x)$ .	Implicitly balances exploration and exploitation through the randomness of the sampled functions, capturing the posterior uncertainty.
Parameter Tuning	Requires careful selection of $\beta_{t}$ to ensure optimal performance and convergence guarantees.	Generally requires less parameter tuning since the balance is managed through posterior sampling.
Computational Considerations	May involve optimization over the acquisition function that includes both mean and variance terms.	Optimization is performed over a single sampled function, which can be computationally efficient but may require multiple samples to stabilize performance.