DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Donghwan | - |
dc.contributor.advisor | 김동환 | - |
dc.contributor.author | Lee, Sucheol | - |
dc.date.accessioned | 2023-06-22T19:33:46Z | - |
dc.date.available | 2023-06-22T19:33:46Z | - |
dc.date.issued | 2022 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=996371&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/308552 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2022.2,[v, 55 p. :] | - |
dc.description.abstract | Modern minimax problems, such as generative adversarial network, adversarial training, and fair training, are usually under a nonconvex-nonconcave setting. There are mainly two types of gradient methods for solving minimax problems: single-step method and multi-step method. However, existing methods either converge slowly or are not guaranteed to converge. In specific, the best known rate for a single-step method is only O(1/k) under a considered structured nonconvex-nonconcave setting, and existing multi-step methods are not guaranteed to converge under the same setting. Therefore, this dissertation provides two new single-step and multi-step methods that have a faster rate and guarantee convergence, respectively, under the structured nonconvex-nonconcave setting. First, we propose an efficient single-step method, named fast extragradient (FEG) method, which, for the first time, achieves the optimal O(1/k$^2$) rate on the squared gradient norm, under the negative comonotonicity condition on the saddle gradient operator. Next, we propose a multi-step method, named semi-anchored multi-step gradient descent ascent (SA-MGDA) method. The SA-MGDA has O(1/k) rate on the squared gradient norm under the weak Minty variational inequality condition on the saddle gradient operator, which is weaker than the negative comonotonicity. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.title | Efficient and convergent gradient methods for structured nonconvex-nonconcave minimax problems | - |
dc.title.alternative | 구조화된 비볼록-비오목 최소 최대화 문제를 위한 효율적이고 수렴하는 경사 방법들 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | 이수철 | - |
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