Noisy Blackbox Optimization using Multi-fidelity Queries: A Tree Search Approach
Rajat Sen, Kirthevasan Kandasamy, Sanjay Shakkottai
Abstract
We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we combine structured state-space exploration through hierarchical partitioning with querying these partitions at multiple fidelities, and develop a multi-fidelity bandit based tree-search algorithm for noisy black-box optimization. We derive simple regret guarantees for our algorithm and validate its performance on real and synthetic datasets.
BibTeX
@InProceedings{pmlr-v89-sen19a,
title = {Noisy Blackbox Optimization using Multi-fidelity Queries: A Tree Search Approach},
author = {Sen, Rajat and Kandasamy, Kirthevasan and Shakkottai, Sanjay},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {2096--2105},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/sen19a/sen19a.pdf},
url = {https://proceedings.mlr.press/v89/sen19a.html},
abstract = {We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we combine structured state-space exploration through hierarchical partitioning with querying these partitions at multiple fidelities, and develop a multi-fidelity bandit based tree-search algorithm for noisy black-box optimization. We derive simple regret guarantees for our algorithm and validate its performance on real and synthetic datasets.}
}