Sampling-Based Zero-Order Optimization Algorithms

Abstract: We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method. Comprehensive numerical experiments demonstrate the algorithm's effectiveness, highlighting three key attributes: (i) Scalability: consistent performance in high-dimensional settings (exceeding 100 dimensions); (ii) Versatility: robust convergence across a diverse suite of benchmark functions, including Schwefel, Rosenbrock, Ackley, Griewank, L\'evy, Rastrigin, and Weierstrass; and (iii) Robustness to discontinuities: reliable performance on non-smooth and discontinuous landscapes. These results illustrate the method's strong potential for black-box optimization in complex, real-world scenarios.