提出新型概率平滑方法，提升全局优化的稳定性和效果。
Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization
- 用对称单峰核与单调比率变换构建通用平滑框架
- 大放大倍数下所有驻点集中于真实最优解，无需递减平滑策略
- 在高维和黑箱攻击任务中表现更稳健，适合追求鲁棒性的研究者
概率平滑是全局优化的标准工具，但现有方法依赖高斯核和特定变换，常导致超参数敏感且鲁棒性差。本文提出一种通用平滑框架，结合灵活的对称单峰核与基于单调比率的变换。在弱条件下，证明平滑目标函数保持全局最大值点，且当放大倍数足够大时，所有驻点均集中在真实最优解附近，无需递减平滑调度。进一步给出了随机梯度上升的显式复杂度界，并证明留一法基线可严格降低方差。在高维基准测试和黑箱对抗攻击任务上的实验表明，该方法具有更强鲁棒性与竞争力。
原文摘要 · Abstract (English)
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general smoothing framework that combines flexible symmetric unimodal kernels with monotonic ratio-based transformations. Under mild conditions, we show that the smoothed objective preserves the global maximizer and that all stationary points concentrate near the true optimum for sufficiently large amplification, without requiring a decreasing smoothing schedule. We further provide explicit complexity bounds for stochastic gradient ascent and show that a leave-one-out baseline provably reduces variance. Experiments on high-dimensional benchmarks and black-box adversarial attacks demonstrate improved robustness and competitive performance.
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