Global Optimization with Parametric Function Approximation

TL;DR

This paper introduces GO-UCB, a parametric optimization algorithm using neural networks that outperforms traditional methods in noisy global optimization tasks, with theoretical guarantees and practical success.

Contribution

The paper proposes GO-UCB, a novel parametric approach for global optimization with noisy oracles, overcoming the curse of dimensionality in existing non-parametric methods.

Findings

Achieves ( ext{(T)}) regret bound

Performs better than Bayesian optimization in experiments

Works well even with model misspecification

Abstract

We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of \~O$(\sqrt{T})$ where $T$ is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than popular Bayesian optimization approaches, even if the model is misspecified.