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Qihang Lin
ADMM without a Fixed Penalty Parameter: Faster Convergence with New Adaptive Penalization
Yi Xu, Mingrui Liu, Qihang Lin, Tianbao Yang
Neural Information Processing Systems http://nips.cc/
Adaptive SVRG Methods under Error Bound Conditions with Unknown Growth Parameter
Yi Xu, Qihang Lin, Tianbao Yang
Neural Information Processing Systems http://nips.cc/
Homotopy Smoothing for Non-Smooth Problems with Lower Complexity than $O(1/\epsilon)$
Yi Xu, Yan Yan, Qihang Lin, Tianbao Yang
In this paper, we develop a novel homotopy smoothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration complexity for solving such non-smooth optimization problems is O(1/ɛ) without any assumption on the strong convexity.
ADMM without a Fixed Penalty Parameter: Faster Convergence with New Adaptive Penalization
Yi Xu, Mingrui Liu, Qihang Lin, Tianbao Yang
Neural Information Processing Systems http://nips.cc/
Adaptive SVRG Methods under Error Bound Conditions with Unknown Growth Parameter
Yi Xu, Qihang Lin, Tianbao Yang
Error bound, an inherent property of an optimization problem, has recently revived in the development of algorithms with improved global convergence without strong convexity. The most studied error bound is the quadratic error bound, which generalizes strong convexity and is satisfied by a large family of machine learning problems. Quadratic error bound have been leveraged to achieve linear convergence in many first-order methods including the stochastic variance reduced gradient (SVRG) method, which is one of the most important stochastic optimization methods in machine learning. However, the studies along this direction face the critical issue that the algorithms must depend on an unknown growth parameter (a generalization of strong convexity modulus) in the error bound. This parameter is difficult to estimate exactly and the algorithms choosing this parameter heuristically do not have theoretical convergence guarantee. To address this issue, we propose novel SVRG methods that automatically search for this unknown parameter on the fly of optimization while still obtain almost the same convergence rate as when this parameter is known. We also analyze the convergence property of SVRG methods under Hölderian error bound, which generalizes the quadratic error bound.