A sequential Monte Carlo approach to Thompson sampling for Bayesian optimization

Abstract

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point to try out. This recommendation is usually selected by optimizing a given acquisition function. After a sufficient number of measurements, a recommendation about the maximum is made. However, a key realization is that the maximum of a Gaussian process is not a deterministic point, but a random variable with a distribution of its own. This distribution cannot be calculated analytically. Our main contribution is an algorithm, inspired by sequential Monte Carlo samplers, that approximates this maximum distribution. Subsequently, by taking samples from this distribution, we enable Thompson sampling to be applied to (armed-bandit) optimization problems with a continuous input space. All this is done without requiring the optimization of a nonlinear acquisition function. Experiments have shown that the resulting optimization method has a competitive performance at keeping the cumulative regret limited.

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• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Expectation Propagation for approximate Bayesian inference
• Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
• Regret Bounds for Deterministic Gaussian Process Bandits

Cited by in corpus (3)

• Efficient acquisition rules for model-based approximate Bayesian computation
• Adaptive Rate of Convergence of Thompson Sampling for Gaussian Process Optimization
• Scalable Bayesian Optimization with Sparse Gaussian Process Models