Optimization Via The Strategic Law Of Large Numbers

This paper proposes a framework for the global optimization of possibly multimodal continuous functions on bounded domains. The authors show that global optimization is equivalent to optimal strategy formation in a two-armed decision model with known distributions, based on a strategic law of large numbers. They establish asymptotically optimal strategies and introduce a class of Strategic Monte Carlo Optimization (SMCO) algorithms that rely on sign-based decisions rather than gradient magnitudes. Theoretical results provide local and global convergence guarantees, and extensive numerical experiments demonstrate strong performance of the proposed algorithms in high-dimensional and challenging optimization settings.