8 papers · 1 filter
Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework
Junwen Qiu, Bohao Ma, Andre Milzarek +1
Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. Thi…
Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioning
Junwen Qiu, Leilei Mei, Junyu Zhang
The global Lipschitz smoothness condition underlies most convergence and complexity analyses via two key consequences: the descent lemma and the gradient Lipschitz continuity. How…
A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis
Junwen Qiu, Ziyang Zeng, Leilei Mei +1
Existing convergence analyses of distributed optimization methods in non-Euclidean geometries typically rely on kernel assumptions: (i) global Lipschitz smoothness and (ii) bi-conv…
A KL-based Analysis Framework with Applications to Non-Descent Optimization Methods
Junwen Qiu, Bohao Ma, Xiao Li +1
We propose a novel analysis framework for non-descent-type optimization methodologies in nonconvex scenarios based on the Kurdyka-Lojasiewicz property. Our framework allows coverin…
A Generalized Version of Chung's Lemma and its Applications
Li Jiang, Xiao Li, Andre Milzarek +1
Chung's Lemma is a classical tool for establishing asymptotic convergence rates of (stochastic) optimization methods under strong convexity-type assumptions and appropriate polynom…
Convergence of SGD with momentum in the nonconvex case: A time window-based analysis
Junwen Qiu, Bohao Ma, Andre Milzarek
The stochastic gradient descent method with momentum (SGDM) is a common approach for solving large-scale and stochastic optimization problems. Despite its popularity, the convergen…