Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization
Provides a more robust and theoretically grounded smoothing method for global optimization, reducing hyperparameter sensitivity for practitioners.
Proposed a probabilistic smoothing framework using flexible kernels and ratio-monotone transforms that preserves global optimizers and concentrates stationary points without a decreasing schedule, achieving improved robustness and competitive performance on high-dimensional benchmarks and adversarial attacks.
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.