Conference proceeding
Level-Set Methods for Finite-Sum Constrained Convex Optimization
INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 80, Vol.80
Proceedings of Machine Learning Research
01/01/2018
Abstract
We consider the constrained optimization where the objective function and the constraints are defined as summation of finitely many loss functions. This model has applications in machine learning such as Neyman-Pearson classification. We consider two level-set methods to solve this class of problems, an existing inexact Newton method and a feasible level-set method. To update the level parameter towards the optimality, both methods require an oracle that generates upper and lower bounds as well as an affine-minorant of the level function. To construct the desired oracle, we reformulate the level function as the value of a saddle-point problem using the conjugate and perspective of the loss functions. Then a stochastic variance-reduced gradient method with a special Bregman divergence is proposed as the oracle for solving that saddle-point problem. The special divergence ensures the proximal mapping in each iteration can be solved in a closed form. The total complexity of both level-set methods using the proposed oracle are analyzed.
Details
- Title: Subtitle
- Level-Set Methods for Finite-Sum Constrained Convex Optimization
- Creators
- Qihang Lin - University of IowaRunchao Ma - Univ Iowa, Management Sci Dept, Iowa City, IA 52242 USATianbao Yang - University of Iowa
- Contributors
- J Dy (Editor)A Krause (Editor)
- Resource Type
- Conference proceeding
- Publication Details
- INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 80, Vol.80
- Publisher
- JMLR-JOURNAL MACHINE LEARNING RESEARCH
- Series
- Proceedings of Machine Learning Research
- ISSN
- 2640-3498
- Number of pages
- 10
- Grant note
- IIS-1545995 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Business Analytics; Computer Science
- Record Identifier
- 9984380454602771
Metrics
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