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Level-Set Methods for Finite-Sum Constrained Convex Optimization
Qihang Lin · Runchao Ma · Tianbao Yang

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #18

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 new 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.

Author Information

Qihang Lin (Univ Iowa)
Runchao Ma (University of Iowa)
Tianbao Yang (The University of Iowa)

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