### Abstract

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function f. Traditional methods 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 regret than strategies which ignore multi-fidelity information. MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

Original language | English (US) |
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Pages (from-to) | 1000-1008 |

Number of pages | 9 |

Journal | Advances in Neural Information Processing Systems |

State | Published - Jan 1 2016 |

Externally published | Yes |

Event | 30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain Duration: Dec 5 2016 → Dec 10 2016 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*Advances in Neural Information Processing Systems*, 1000-1008.

**Gaussian process bandit optimisation with multi-fidelity evaluations.** / Kandasamy, Kirthevasan; Dasarathy, Gautam; Oliva, Junier; Schneider, Jeff; Póczos, Barnabs.

Research output: Contribution to journal › Conference article

*Advances in Neural Information Processing Systems*, pp. 1000-1008.

}

TY - JOUR

T1 - Gaussian process bandit optimisation with multi-fidelity evaluations

AU - Kandasamy, Kirthevasan

AU - Dasarathy, Gautam

AU - Oliva, Junier

AU - Schneider, Jeff

AU - Póczos, Barnabs

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function f. Traditional methods 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 regret than strategies which ignore multi-fidelity information. MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

AB - In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function f. Traditional methods 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 regret than strategies which ignore multi-fidelity information. MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

UR - http://www.scopus.com/inward/record.url?scp=85018876167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018876167&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85018876167

SP - 1000

EP - 1008

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

ER -