Noisy Blackbox Optimization using Multi-fidelity Queries: A Tree Search Approach

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.