Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization
2026-05-26 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a new method to make tough optimization problems easier by smoothing the objective function in a more flexible way than usual. Their approach uses different smoothing shapes and transformations, which helps keep the best solution intact and makes finding it more reliable. They also show that their method works well with standard algorithms like stochastic gradient ascent and reduces randomness in the process. Tests on challenging problems and security attacks show their method is robust and performs competitively.
Probabilistic smoothingGlobal optimizationSymmetric unimodal kernelsMonotonic transformationsStochastic gradient ascentVariance reductionStationary pointsBlack-box adversarial attacksComplexity bounds
Authors
Kukyoung Jang, Taehyun Cho, Junrui Zhang, Ping Xu, Kyungjae Lee
Abstract
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.