A Computationally Efficient Approach to Black-box Optimization using Gaussian Process Models

by   Sudeep Salgia, et al.

We consider the sequential optimization of an unknown function from noisy feedback using Gaussian process modeling. A prevailing approach to this problem involves choosing query points based on finding the maximum of an upper confidence bound (UCB) score over the entire domain of the function. Due to the multi-modal nature of the UCB, this maximization can only be approximated, usually using an increasingly fine sequence of discretizations of the entire domain, making such methods computationally prohibitive. We propose a general approach that reduces the computational complexity of this class of algorithms by a factor of O(T^2d-1) (where T is the time horizon and d the dimension of the function domain), while preserving the same regret order. The significant reduction in computational complexity results from two key features of the proposed approach: (i) a tree-based localized search strategy rooted in the methodology of domain shrinking to achieve increasing accuracy with a constant-size discretization; (ii) a localized optimization with the objective relaxed from a global maximizer to any point with value exceeding a given threshold, where the threshold is updated iteratively to approach the maximum as the search deepens. More succinctly, the proposed optimization strategy is a sequence of localized searches in the domain of the function guided by an iterative search in the range of the function to approach the maximum.


page 1

page 2

page 3

page 4


Ada-BKB: Scalable Gaussian Process Optimization on Continuous Domain by Adaptive Discretization

Gaussian process optimization is a successful class of algorithms (e.g. ...

Gaussian Process bandits with adaptive discretization

In this paper, the problem of maximizing a black-box function f:X→R is s...

MISO-wiLDCosts: Multi Information Source Optimization with Location Dependent Costs

This paper addresses black-box optimization over multiple information so...

Analysis of Thompson Sampling for Gaussian Process Optimization in the Bandit Setting

We consider the global optimization of a function over a continuous doma...

Regret Bounds for Gaussian-Process Optimization in Large Domains

The goal of this paper is to characterize Gaussian-Process optimization ...

Safe global optimization of expensive noisy black-box functions in the δ-Lipschitz framework

In this paper, the problem of safe global maximization (it should not be...

The Localized Subtraction Approach For EEG and MEG Forward Modeling

In FEM-based EEG and MEG source analysis, the subtraction approach has b...

Please sign up or login with your details

Forgot password? Click here to reset