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Article overview
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Stochastic Optimization for Non-convex Inf-Projection Problems | | Yan Yan
; Yi Xu
; Lijun Zhang
; Xiaoyu Wang
; Tianbao Yang
; | | Date: |
27 Aug 2019 | | Abstract: | In this paper, we study a family of non-convex and possibly non-smooth
inf-projection minimization problems, where the target objective function is
equal to minimization of a joint function over another variable. This problem
includes difference of convex (DC) functions and a family of bi-convex
functions as special cases. We develop stochastic algorithms and establish
their first-order convergence for finding a (nearly) stationary solution of the
target non-convex function under different conditions of the component
functions. To the best of our knowledge, this is the first work that
comprehensively studies stochastic optimization of non-convex inf-projection
minimization problems with provable convergence guarantee. Our algorithms
enable efficient stochastic optimization of a family of non-decomposable DC
functions and a family of bi-convex functions. To demonstrate the power of the
proposed algorithms we consider an important application in variance-based
regularization, and experiments verify the effectiveness of our inf-projection
based formulation and the proposed stochastic algorithm in comparison with
previous stochastic algorithms based on the min-max formulation for achieving
the same effect. | | Source: | arXiv, 1908.9941 | | Services: | Forum | Review | PDF | Favorites | |
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