Model-based Gradient Search using the Plackett-Luce model

Valentino Santucci, Josu Ceberio

Abstract: Computational optimization and optimization algorithms form a cornerstone area of computer science that has been extensively explored due to its myriad applications in many practical and real-world scenarios. At a high level, we can categorize computational optimization algorithms into two main classes: white-box and black-box algorithms. While the former require a certain degree of knowledge about the problem domain, the latter are more versatile and rely solely on basic domain information, such as the structure or representation of a solution. Perhaps, the most prominent examples of white-box algorithms are those which iteratively refine a solution based on the gradient of the objective function at hand. While widely used, particularly in the field of machine learning, these techniques have limited applicability in other domains where gradient information is unavailable. This is the case of Combinatorial Optimization Problems (COPs), where the domain consists of discrete solutions and, for this reason, the concept of gradient is not applicable.