Article2011

Portfolio allocation for Bayesian optimization

Matthew D. Hoffman · Eric Brochu · Nando de Freitas

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Advanced Bandit Algorithms Research Reinforcement Learning in Robotics Advanced Multi-Objective Optimization Algorithms

Abstract

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the posterior estimate of the objective. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm’s performance. 1

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References

2006Prediction, Learning, and Games 1998Model-Based Geostatistics 2012Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting 2010A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning 1964A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise 2002Gambling in a rigged casino: The adversarial multi-armed bandit problem 2011Convergence rates of efficient global optimization algorithms 2010Best Arm Identification in Multi-Armed Bandits

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