Multi-fidelity Bayesian Optimisation with Continuous Approximations
This addresses the challenge of costly evaluations in applications like hyper-parameter tuning for neural networks, offering a more efficient optimization approach, though it is incremental as it extends existing multi-fidelity methods to continuous settings.
The paper tackles the problem of expensive function evaluations in black-box optimization by developing BOCA, a multi-fidelity Bayesian optimization method that handles continuous approximations, such as varying data sizes and training iterations, and shows it achieves better regret than methods ignoring these approximations in synthetic and real experiments.
Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, \emph{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. In many practical applications however, 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 $(N,T)$. 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.