Bayesian functional optimisation with shape prior

TL;DR

This paper introduces a Bayesian optimisation framework for functional problems involving control variables over time, using Bernstein polynomial basis and shape priors to efficiently find optimal solutions in expensive black-box experiments.

Contribution

It presents a novel Bayesian optimisation method that dynamically adjusts polynomial degree and incorporates shape priors for functional control problems.

Findings

Effective in short polymer fibre design optimization.

Successfully optimizes learning rate schedules for deep networks.

Demonstrates efficiency in reducing experimental runs.

Abstract

Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.