7 papers · 1 filter
Nearly Optimal Risk Minimization
Zhichao Jia, Guanghui Lan, Zhe Zhang
Convex risk measures play a foundational role in the area of stochastic optimization. However, in contrast to risk neutral models, their applications are still limited due to the l…
Projected gradient methods for nonconvex and stochastic smooth optimization: new complexities and auto-conditioned stepsizes
Guanghui Lan, Tianjiao Li, Yangyang Xu
We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis…
Uniformly Optimal and Parameter-free First-order Methods for Convex and Function-constrained Optimization
Qi Deng, Guanghui Lan, Zhenwei Lin
This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by…
High-order Accumulative Regularization for Gradient Minimization in Convex Programming
Yao Ji, Guanghui Lan
This paper develops a unified high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often ex…
Optimal and parameter-free gradient minimization methods for convex and nonconvex optimization
Guanghui Lan, Yuyuan Ouyang, Zhe Zhang
We propose novel optimal and parameter-free algorithms for computing an approximate solution with small (projected) gradient norm. Specifically, for computing an approximate soluti…
Auto-conditioned primal-dual hybrid gradient method and alternating direction method of multipliers
Guanghui Lan, Tianjiao Li
Line search procedures are often employed in primal-dual methods for bilinear saddle point problems, especially when the norm of the linear operator is large or difficult to comput…