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

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  • Abdullah Al-Dujaili

    (MIT)

  • S. Suresh

    (Nanyang Technological University)

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 $$\epsilon $$ 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.

Suggested Citation

  • Abdullah Al-Dujaili & S. Suresh, 2019. "Revisiting norm optimization for multi-objective black-box problems: a finite-time analysis," Journal of Global Optimization, Springer, vol. 73(3), pages 659-673, March.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:3:d:10.1007_s10898-018-0709-z
    DOI: 10.1007/s10898-018-0709-z
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    References listed on IDEAS

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    1. Abdullah Al-Dujaili & S. Suresh & N. Sundararajan, 2016. "MSO: a framework for bound-constrained black-box global optimization algorithms," Journal of Global Optimization, Springer, vol. 66(4), pages 811-845, December.
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