Online Dynamic Submodular Optimization

Fuente: arXiv
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Autori principali: Lesage-Landry, Antoine, Pallage, Julien
Natura: Preprint
Pubblicazione: 2023
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author Lesage-Landry, Antoine
Pallage, Julien
author_facet Lesage-Landry, Antoine
Pallage, Julien
contents We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function to avoid the NP-hardness of the original problem. We extend OSGA to a generic approximation function. We show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, we design the online submodular projected gradient descent (OSPGD) by leveraging the Lovaśz extension. We obtain a regret bound that is akin to the conventional online gradient descent (OGD). Finally, we numerically test our algorithms in two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.
format Preprint
id arxiv_https___arxiv_org_abs_2306_10835
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Online Dynamic Submodular Optimization
Lesage-Landry, Antoine
Pallage, Julien
Optimization and Control
Machine Learning
We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function to avoid the NP-hardness of the original problem. We extend OSGA to a generic approximation function. We show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, we design the online submodular projected gradient descent (OSPGD) by leveraging the Lovaśz extension. We obtain a regret bound that is akin to the conventional online gradient descent (OGD). Finally, we numerically test our algorithms in two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.
title Online Dynamic Submodular Optimization
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2306.10835