Communication Dans Un Congrès Année : 2022

Robustness in Multi-Objective Submodular Optimization: a Quantile Approach

Résumé

The optimization of multi-objective submodular systems appears in a wide variety of applications. However, there are currently very few techniques which are able to provide a robust allocation to such systems. In this work, we propose to design and analyse novel algorithms for the robust allocation of submodular systems through lens of quantile maximization. We start by observing that identifying an exact solution for this problem is computationally intractable. To tackle this issue, we propose a proxy for the quantile function using a softmax formulation, and show that this proxy is well suited to submodular optimization. Based on this relaxation, we propose a novel and simple algorithm called SOFTSAT. Theoretical properties are provided for this algorithm as well as novel approximation guarantees. Finally, we provide numerical experiments showing the efficiency of our algorithm with regards to state-of-the-art methods in a test bed of real-world applications, and show that SOFTSAT is particularly robust and well-suited to online scenarios.

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Dates et versions

hal-03896023 , version 1 (13-12-2022)

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  • HAL Id : hal-03896023 , version 1

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Cédric Malherbe, Kevin Scaman. Robustness in Multi-Objective Submodular Optimization: a Quantile Approach. ICML 2022 - 39th International Conference on Machine Learning, Jul 2022, Baltimore, United States. ⟨hal-03896023⟩
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