### Abstract

Bandit methods for black-box optimisation, such as Bayesian optimisation, arc used in a variety of applications including hyper-parameter tuning and experiment design. Recently, multi-fidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data N and/or few training iterations T. Here, the approximations are best viewed as arising out of a continuous two dimensional space (iV, T). In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

Original language | English (US) |
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Title of host publication | 34th International Conference on Machine Learning, ICML 2017 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 2861-2878 |

Number of pages | 18 |

ISBN (Electronic) | 9781510855144 |

State | Published - Jan 1 2017 |

Externally published | Yes |

Event | 34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia Duration: Aug 6 2017 → Aug 11 2017 |

### Publication series

Name | 34th International Conference on Machine Learning, ICML 2017 |
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Volume | 4 |

### Conference

Conference | 34th International Conference on Machine Learning, ICML 2017 |
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Country | Australia |

City | Sydney |

Period | 8/6/17 → 8/11/17 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Human-Computer Interaction
- Software

### Cite this

*34th International Conference on Machine Learning, ICML 2017*(pp. 2861-2878). (34th International Conference on Machine Learning, ICML 2017; Vol. 4). International Machine Learning Society (IMLS).

**Multi-fidelity Bayesian optimisation with continuous approximations.** / Kandasamy, Kirthevasan; Dasarathy, Gautam; Schneider, Jeff; Póczos, Barnabás.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*34th International Conference on Machine Learning, ICML 2017.*34th International Conference on Machine Learning, ICML 2017, vol. 4, International Machine Learning Society (IMLS), pp. 2861-2878, 34th International Conference on Machine Learning, ICML 2017, Sydney, Australia, 8/6/17.

}

TY - GEN

T1 - Multi-fidelity Bayesian optimisation with continuous approximations

AU - Kandasamy, Kirthevasan

AU - Dasarathy, Gautam

AU - Schneider, Jeff

AU - Póczos, Barnabás

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Bandit methods for black-box optimisation, such as Bayesian optimisation, arc used in a variety of applications including hyper-parameter tuning and experiment design. Recently, multi-fidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data N and/or few training iterations T. Here, the approximations are best viewed as arising out of a continuous two dimensional space (iV, T). In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

AB - Bandit methods for black-box optimisation, such as Bayesian optimisation, arc used in a variety of applications including hyper-parameter tuning and experiment design. Recently, multi-fidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data N and/or few training iterations T. Here, the approximations are best viewed as arising out of a continuous two dimensional space (iV, T). In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

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M3 - Conference contribution

AN - SCOPUS:85048435897

T3 - 34th International Conference on Machine Learning, ICML 2017

SP - 2861

EP - 2878

BT - 34th International Conference on Machine Learning, ICML 2017

PB - International Machine Learning Society (IMLS)

ER -