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Stochastic Optimization for Non-convex Inf-Projection Problems
Yan Yan · Yi Xu · Lijun Zhang · Wang Xiaoyu · Tianbao Yang

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 06:00 PM -- 06:45 PM (PDT) @

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 include 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. 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.

Author Information

Yan Yan (the University of Iowa)
Yi Xu (Alibaba Group (U.S.) Inc.)
Lijun Zhang (Nanjing University)
Wang Xiaoyu (The Chinese University of Hong Kong (Shenzhen))
Tianbao Yang (The University of Iowa)

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