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Dabeen Lee (이다빈), Non-smooth and Hölder-smooth submodular optimization

Thursday, October 27, 2022 @ 4:15 PM - 5:15 PM KST

Room 1501, Bldg. E6-1, KAIST

We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves an [(1−1/e)OPT−ϵ] guarantee when the function is monotone and Hölder-smooth, meaning that it admits a Hölder-continuous gradient. For functions that are non-differentiable or non-smooth, we propose a variant of the mirror-prox algorithm that attains an [(1/2)OPT−ϵ] guarantee. We apply our algorithmic frameworks to robust submodular maximization and distributionally robust submodular maximization under Wasserstein ambiguity. In particular, the mirror-prox method applies to robust submodular maximization to obtain a single feasible solution whose value is at least (1/2)OPT−ϵ. For distributionally robust maximization under Wasserstein ambiguity, we deduce and work over a submodular-convex maximin reformulation whose objective function is Hölder-smooth, for which we may apply both the continuous greedy method and the mirror-prox method.
Joint work with Duksang Lee and Nam Ho-Ngyuen.


Thursday, October 27, 2022
4:15 PM - 5:15 PM KST
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Room 1501, Bldg. E6-1, KAIST


Andreas Holmsen
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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