Multi-fidelity Gaussian Process Bandit Optimisation

By Kirthevasan Kandasamy, Gautam Dasarathy, Junier B. Oliva, Jeff Schneider, Barnab'as P'oczos. 2016

87 citations recorded by the source corpus.

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

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Citations in the corpus

Multi-Fidelity Automatic Hyper-Parameter Tuning via Transfer Series Expansion (2019, methodology): “Multi-fidelity optimization has been deeply studied on surrogate model optimization such as Bayesian optimization (Huang et al. 2006; Kandasamy et al. 2016; 2017).”
Neural Architecture Search with Bayesian Optimisation and Optimal Transport (2018, background): “[18] Kirthevasan Kandasamy, Gautam Dasarathy, Junier B Oliva, Jeff Schneider, and Barnabas Poczos.”
Multi-fidelity Bayesian Optimisation with Continuous Approximations (2017, methodology): “We compare BOCA to the following four baselines: (i) GP-UCB , (ii) the GP-EI criterion in BO (Jones et al., 1998), (iii) MF-GP-UCB (Kandasamy et al., 2016a) and (iv) MF-SKO , the multi-ﬁdelity sequential kriging optimisation method from Huang et al. (2006).”
Multi-Information Source Optimization (2016, background): “Besides, interesting variants of the MISO problem have been studied recently: Kandasamy et al. [2016] examined an alternative objective for multifidelity settings that asks to minimize the cumulative regret over a series of function evaluations: besides classification problems they also presented an”
Multi-Fidelity Black-Box Optimization with Hierarchical Partitions (2018, methodology): “Kandasamy et al. (2016c) propose and analyse a UCB style multi-fidelity algorithm for the K-armed bandit setting assuming a finite number of approximations to the K arms.”
Recent Advances in Bayesian Optimization (2022, methodology): “[90] adopted MF-GP-UCB to explore the search space at lower idelities, and then exploit the high idelities in successively smaller regions.”