Batched Gaussian Process Bandit Optimization via Determinantal Point Processes

TL;DR

This paper introduces a novel batch Bayesian optimization method using Determinantal Point Processes to model diversity, enabling efficient parallel evaluations and outperforming existing approaches in various tasks.

Contribution

It proposes a new DPP-based approach for batch Gaussian Process bandit optimization with learned kernels, improving regret bounds and parallel exploration efficiency.

Findings

DPP-based methods outperform state-of-the-art in synthetic and real-world tasks.

Learned kernels enhance diversity modeling in batch optimization.

DPP sampling provides superior exploration strategies.

Abstract

Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function requires training a model which may involve days or even weeks of computation. Most methods for this so-called "Bayesian optimization" only allow sequential exploration of the parameter space. However, it is often desirable to propose batches or sets of parameter values to explore simultaneously, especially when there are large parallel processing facilities at our disposal. Batch methods require modeling the interaction between the different evaluations in the batch, which can be expensive in complex scenarios. In this paper, we propose a new approach for parallelizing Bayesian optimization by modeling the diversity of a batch via Determinantal point processes (DPPs) whose kernels are learned automatically. This allows us to generalize a previous result as well as prove better regret bounds based on DPP sampling. Our experiments on a variety of synthetic and real-world robotics and hyper-parameter optimization tasks indicate that our DPP-based methods, especially those based on DPP sampling, outperform state-of-the-art methods.