SGD is reformulated via a master equation from discrete updates, producing a discrete Fokker-Planck equation that predicts non-stationary variance growth proportional to learning rate in flat Hessian directions.
On linear convergence in smooth convex-concave bilinearly- coupled saddle-point optimization: Lower bounds and optimal algorithms
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Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.
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Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics
SGD is reformulated via a master equation from discrete updates, producing a discrete Fokker-Planck equation that predicts non-stationary variance growth proportional to learning rate in flat Hessian directions.
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Optimal Projection-Free Adaptive SGD for Matrix Optimization
Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.