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 $\epsilon$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.11020
- arXiv:
- arXiv:1804.11020
- Bibcode:
- 2018arXiv180411020A
- Keywords:
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- Mathematics - Optimization and Control
- E-Print:
- submitted to Journal of Global Optimization. This article's notation and terminology is based on arXiv:1612.08412