ITSO: a novel inverse transform sampling-based optimization algorithm for stochastic search

Abstract

Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods and Engineering and Business applications. Following recent works on AI's theoretical deficiencies, a rigour context for the optimization problem of a black-box objective function is developed. The algorithm stems directly from the theory of probability, instead of presumed inspiration. Thus the convergence properties of the proposed methodology are inherently stable. In particular, the proposed optimizer utilizes an algorithmic implementation of the n-dimensional inverse transform sampling as a search strategy. No control parameters are required to be tuned, and the trade-off among exploration and exploitation is, by definition, satisfied. A theoretical proof is provided, concluding that when falling into the proposed framework, either directly or incidentally, any optimization algorithm converges. The numerical experiments verify the theoretical results on the efficacy of the algorithm apropos reaching the sought optimum.