# Bayesian functional optimisation with shape prior

arXiv: https://arxiv.org/abs/1809.07260 · HTML: https://mlsanity.com/paper/1809.07260/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2018.

## Built on by (most cited first, 3 of 3)

- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Thompson Sampling in Function Spaces via Neural Operators](https://mlsanity.com/paper/2506.21894/) (2025)
- [Active Subspaces in Infinite Dimension](https://mlsanity.com/paper/2510.11871/) (2025)

## Abstract (arXiv)

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.