Research map / Optimization / Nonconvex and smooth optimization
High Probability Convergence of Stochastic Gradient Methods
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Bregman-diameter-dependent high-probability analysis with a white-box MGF argument that scales with initial distance D_psi(x*,x_1) (SMD, step sizes analogous to standard) | Stochastic mirror descent (convex, Lipschitz) · convex stochastic optimization, sub-Gaussian noise | convergence rate (qualitative, no empirical numbers) | No clear effect |
| Remove bounded-gradient assumption in AdaGrad-Norm analysis by using proxy step size and martingale concentration | AdaGrad-Norm (non-convex, smooth) · non-convex smooth optimization, sub-Gaussian noise | high-probability gradient norm bound (theoretical) | Helped |
| Extend the AdaGrad-Norm analysis to per-coordinate AdaGrad | AdaGrad (per-coordinate) · non-convex smooth optimization, sub-Gaussian noise | high-probability gradient bound (theoretical) | Helped |
| Use time-varying step size 1/(L sqrt t) for SGD when T unknown, with log T additive instead of multiplicative | SGD (non-convex) · non-convex smooth optimization, sub-Gaussian noise | high-probability rate dependence on log T | Helped |
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