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An Improved Analysis of Gradient Tracking for Decentralized Machine Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Analyze Gradient Tracking with the new proof technique instead of the prior bound | Gradient Tracking · Strongly convex stochastic optimization | iterations to ε-accuracy: from \cO(p^{-3/2}) to \cO(p^{-1/2}c^{-1}) in the general stochastic case | Helped |
| Analyze Gradient Tracking with the new proof technique instead of the prior bound | Gradient Tracking · Strongly convex noiseless optimization | iterations to ε-accuracy: from \cO(p^{-2}) to \cO(p^{-1}c^{-1}) | Helped |
| Use the improved analysis with c constant rather than the prior p-dependent bound | Gradient Tracking · Strongly convex stochastic optimization | iterations to ε-accuracy: factor of \smash{\frac{c}{p}} \geq 1 | Helped |
| Use the improved analysis with c constant rather than the prior graph dependence | Gradient Tracking · Non-convex stochastic optimization | iterations to ε-accuracy: prior \cO(p^{-3}) dependence; proposed \frac{L}{pc\varepsilon} | Helped |
| Vary p while keeping c and the stepsize constant | Gradient Tracking · Quadratic stochastic objective on interpolated ring and fully connected topologies | steady-state loss | Mixed |
| Reduce self-weights to vary c while keeping p and the stepsize constant | Gradient Tracking · Quadratic stochastic objective on a ring topology | steady-state loss | Mixed |
| Use larger self-weights to increase c | Gradient Tracking · Decentralized optimization on networks | convergence rate | Helped |
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