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math.OC2023
Convex and Non-convex Optimization Under Generalized Smoothness
Haochuan Li, Jian Qian, Yi Tian +2
Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Rece…
math.OC2023
Convergence of Adam Under Relaxed Assumptions
Haochuan Li, Alexander Rakhlin, Ali Jadbabaie
In this paper, we provide a rigorous proof of convergence of the Adaptive Moment Estimate (Adam) algorithm for a wide class of optimization objectives. Despite the popularity and e…
math.OC2021★ 10 cited
Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization
Haochuan Li, Yi Tian, Jingzhao Zhang +1
We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minim…