Surrogate‐Free Annealing Random Search for Continuous Stochastic Optimization

ABSTRACT Optimizing blackbox stochastic systems, where only outputs are observable, is challenging due to difficulties in estimating objective function values. Surrogate‐based methods, such as interpolation, are widely used but struggle with stochastic noise and high computational costs. To overcome these limitations, we propose surrogate‐free annealing random search (SFARS), a novel algorithm that eliminates explicit surrogate models. SFARS employs a value aggregation mechanism based on a predefined discrete point set, enabling efficient Monte Carlo estimators. Theoretical analysis establishes a finite‐time probability error bound and guarantees almost sure global convergence with a sub‐exponential rate. Numerical experiments demonstrate superior efficiency and robustness, particularly in high‐noise environments.