Certified Multi-Fidelity Zeroth-Order Optimization

• URL: http://arxiv.org/abs/2308.00978v2
• Date: Fri, 11 Oct 2024 08:11:15 GMT
• Title: Certified Multi-Fidelity Zeroth-Order Optimization
• Authors: Étienne de Montbrun, Sébastien Gerchinovitz,
• Abstract summary: We consider the problem of multi-fidelity zeroth-order optimization, where one can evaluate a function $f$ at various approximation levels. We propose a certified variant of the MFDOO algorithm and derive a bound on its cost complexity for any Lipschitz function $f$. We also prove an $f$-dependent lower bound showing that this algorithm has a near-optimal cost complexity.
• Score: 4.450536872346658
• License:
• Abstract: We consider the problem of multi-fidelity zeroth-order optimization, where one can evaluate a function $f$ at various approximation levels (of varying costs), and the goal is to optimize $f$ with the cheapest evaluations possible. In this paper, we study certified algorithms, which are additionally required to output a data-driven upper bound on the optimization error. We first formalize the problem in terms of a min-max game between an algorithm and an evaluation environment. We then propose a certified variant of the MFDOO algorithm and derive a bound on its cost complexity for any Lipschitz function $f$. We also prove an $f$-dependent lower bound showing that this algorithm has a near-optimal cost complexity. As a direct example, we close the paper by addressing the special case of noisy (stochastic) evaluations, which corresponds to $\eps$-best arm identification in Lipschitz bandits with continuously many arms.

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