Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity

• URL: http://arxiv.org/abs/2605.31346v1
• Date: Fri, 29 May 2026 14:24:54 GMT
• Title: Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity
• Abstract summary: Black-box optimization is applied when gradients are unavailable and objective evaluations rely on expensive simulations.<n>We show how the choice of oracle type, noise model, and optimization scheme induces explicit wall-clock-optimal choices for the algorithmic parameters.
• Score: 68.54852541944625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Zeroth-order (black-box) optimization is applied when gradients are unavailable and objective evaluations rely on expensive simulations. In many such applications, the oracle fidelity is tunable: higher-accuracy queries reduce noise but incur higher computational costs. To capture this trade-off, we study an accuracy-aware wall-clock model where each query with fidelity $δ$ has a cost $c(δ)$, and we minimize the total time $T_{\mathrm{total}} = \sum_{k=1}^{N} c(δ_k)$, subject to a target accuracy constraint. We show how the choice of oracle type, noise model, and optimization scheme induces explicit wall-clock-optimal choices for the algorithmic parameters. For instance, we demonstrate that accelerated methods can be wall-clock inferior to non-accelerated schemes. Furthermore, we characterize the conditions under which a constant fidelity strategy is optimal in the Big-O sense. Our framework provides a unified methodology to translate convergence guarantees into practical fidelity and batching recommendations.

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