Power Homotopy for Zeroth-Order Non-Convex Optimizations

• URL: http://arxiv.org/abs/2511.13592v1
• Date: Mon, 17 Nov 2025 16:54:30 GMT
• Title: Power Homotopy for Zeroth-Order Non-Convex Optimizations
• Authors: Chen Xu,
• Abstract summary: GS-Power is a novel zeroth-order method for non-dimensional optimization problems.<n>It consistently ranks among the top three across a suite of competing algorithms.<n>It achieved first place at least-likely targeted black-box attacks against images from ImageNet.
• Score: 5.737648067191245
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We introduce GS-PowerHP, a novel zeroth-order method for non-convex optimization problems of the form $\max_{x \in \mathbb{R}^d} f(x)$. Our approach leverages two key components: a power-transformed Gaussian-smoothed surrogate $F_{N,σ}(μ) = \mathbb{E}_{x\sim\mathcal{N}(μ,σ^2 I_d)}[e^{N f(x)}]$ whose stationary points cluster near the global maximizer $x^*$ of $f$ for sufficiently large $N$, and an incrementally decaying $σ$ for enhanced data efficiency. Under mild assumptions, we prove convergence in expectation to a small neighborhood of $x^*$ with the iteration complexity of $O(d^2 \varepsilon^{-2})$. Empirical results show our approach consistently ranks among the top three across a suite of competing algorithms. Its robustness is underscored by the final experiment on a substantially high-dimensional problem ($d=150,528$), where it achieved first place on least-likely targeted black-box attacks against images from ImageNet, surpassing all competing methods.

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