Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis

Abstract

The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the solutions, or studied their asymptotic behaviour. In this paper, we revisit the Tchebycheff weighted method in a hierarchical bandits setting and provide a finite-time bound on the Pareto-compliant additive ϵ-indicator. To the best of our knowledge, this paper is one of few that establish a link between weighted sum methods and quality indicators in finite time.