# Revisiting Norm Optimization for Multi-Objective Black-Box Problems: A Finite-Time Analysis

arXiv: https://arxiv.org/abs/1804.11020 · HTML: https://mlsanity.com/paper/1804.11020/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

## Built on by (most cited first, 2 of 2)

- [A Nested Weighted Tchebycheff Multi-Objective Bayesian Optimization Approach for Flexibility of Unknown Utopia Estimation in Expensive Black-box Design Problems](https://mlsanity.com/paper/2110.11070/) (2021)
- [Non-linear Multi-objective Optimization with Probabilistic Branch and Bound](https://mlsanity.com/paper/2506.04554/) (2025)

## Abstract (arXiv)

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.