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Sample-Efficient Bayesian Optimization with Transfer Learning for Heterogeneous Search Spaces

Aryan Deshwal, Sait Cakmak, Yuhou Xia, David Eriksson

TL;DR

The first approach leverages a Gaussian process (GP) model with a conditional kernel to transfer information between different search spaces and treats the missing parameters as hyperparameters of the GP model that can be inferred jointly with the other GP hyperparameters or set to fixed values.

Abstract

Bayesian optimization (BO) is a powerful approach to sample-efficient optimization of black-box functions. However, in settings with very few function evaluations, a successful application of BO may require transferring information from historical experiments. These related experiments may not have exactly the same tunable parameters (search spaces), motivating the need for BO with transfer learning for heterogeneous search spaces. In this paper, we propose two methods for this setting. The first approach leverages a Gaussian process (GP) model with a conditional kernel to transfer information between different search spaces. Our second approach treats the missing parameters as hyperparameters of the GP model that can be inferred jointly with the other GP hyperparameters or set to fixed values. We show that these two methods perform well on several benchmark problems.

Sample-Efficient Bayesian Optimization with Transfer Learning for Heterogeneous Search Spaces

TL;DR

The first approach leverages a Gaussian process (GP) model with a conditional kernel to transfer information between different search spaces and treats the missing parameters as hyperparameters of the GP model that can be inferred jointly with the other GP hyperparameters or set to fixed values.

Abstract

Bayesian optimization (BO) is a powerful approach to sample-efficient optimization of black-box functions. However, in settings with very few function evaluations, a successful application of BO may require transferring information from historical experiments. These related experiments may not have exactly the same tunable parameters (search spaces), motivating the need for BO with transfer learning for heterogeneous search spaces. In this paper, we propose two methods for this setting. The first approach leverages a Gaussian process (GP) model with a conditional kernel to transfer information between different search spaces. Our second approach treats the missing parameters as hyperparameters of the GP model that can be inferred jointly with the other GP hyperparameters or set to fixed values. We show that these two methods perform well on several benchmark problems.
Paper Structure (23 sections, 2 equations, 3 figures, 1 algorithm)

This paper contains 23 sections, 2 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Transfer Learning in Bayesian Optimization (BO)
  4. BO with Heterogeneous Search Spaces
  5. Background
  6. Bayesian Optimization
  7. Bayesian Optimization with Transfer Learning
  8. BO with Transfer Learning for Heterogeneous Search Spaces
  9. MTGP with Conditional Kernels
  10. Tree-Structured Representation of Heterogeneous Search Spaces
  11. Conditional kernel
  12. MTGP with Conditional Kernels
  13. MTGP with Imputed Values
  14. Experiments
  15. Methods
  16. ...and 8 more sections

Figures (3)

  • Figure 1: The tree-based representation and the corresponding kernels of the search spaces $\mathcal{X}_{1}, \mathcal{X}_{2}$ and $\mathcal{X}_{3}$ given in Sec. \ref{['sec:background']}.
  • Figure 2: (Left) The Learned Imputed MTGP performs the best on the 6D Hartmann problem. (Middle/Right) The MTGP-based methods outperform Vanilla BO and Random Search on the 11D Ranger and 6D Rpart problems. Each experiment employs 30 source task trials.
  • Figure 3: Ablation study for varying the number of trials for each source task on the 11D Ranger problem. We observe that the MTGP with conditional kernels performs the best when only a small number of source trials are available. As more source data is available, the Learned Imputed MTGP and MTGP on common parameters perform the best.