Multi-objective Bayesian Optimization using Pareto-frontier Entropy

06/01/2019
by   Shinya Suzuki, et al.
0

We propose Pareto-frontier entropy search (PFES) for multi-objective Bayesian optimization (MBO). Unlike the existing entropy search for MBO which considers the entropy of the input space, we define the entropy of Pareto-frontier in the output space. By using a sampled Pareto-frontier from the current model, PFES provides a simple formula for directly evaluating the entropy. Besides the usual MBO setting, in which all the objectives are simultaneously observed, we also consider the "decoupled" setting, in which the objective functions can be observed separately. PFES can easily derive an acquisition function for the decoupled setting through the entropy of the marginal density for each output variable. For the both settings, by conditioning on the sampled Pareto-frontier, dependence among different objectives arises in the entropy evaluation. PFES can incorporate this dependency into the acquisition function, while the existing information-based MBO employs an independent Gaussian approximation. Our numerical experiments show effectiveness of PFES through synthetic functions and real-world datasets from materials science.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/17/2015

Predictive Entropy Search for Multi-objective Bayesian Optimization

We present PESMO, a Bayesian method for identifying the Pareto set of mu...
research
06/01/2023

BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

Many scientific and industrial applications require joint optimization o...
research
04/11/2022

{PF}^2ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization Under Unknown Constraints

We present Parallel Feasible Pareto Frontier Entropy Search ({PF}^2ES) –...
research
11/02/2020

Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach

We study the novel problem of blackbox optimization of multiple objectiv...
research
06/24/2020

Pareto Active Learning with Gaussian Processes and Adaptive Discretization

We consider the problem of optimizing a vector-valued objective function...
research
05/19/2015

Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes

This paper introduces the necessary and sufficient conditions that surro...
research
07/28/2023

Learning Compliant Stiffness by Impedance Control-Aware Task Segmentation and Multi-objective Bayesian Optimization with Priors

Rather than traditional position control, impedance control is preferred...

Please sign up or login with your details

Forgot password? Click here to reset