Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration
In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of sqrt{K} for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization
This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization. The known regret upper bounds for the widely used GP batched upper confidence bound and GP batched Thompson sampling (GP-BTS)…
Regret Analysis for Randomized Gaussian Process Upper Confidence Bound
Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows GP. One notable drawback of GP-UCB is that the …
Bayesian OptimizationMean Square Prediction Error of Misspecified Gaussian Process Models
Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide gu…
PredictionregressionvalidOn Batch Bayesian Optimization
We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical…
Bayesian OptimizationThompson SamplingThe reparameterization trick for acquisition functions
Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guid…
Bayesian Optimizationglobal-optimization