Research map / Optimization / Nonconvex and smooth optimization
SGD and Hogwild! Convergence Without the Bounded Gradients Assumption
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Assume each stochastic loss realization is L-smooth and convex instead of assuming uniformly bounded stochastic gradients | SGD · Strongly convex stochastic optimization | almost-sure convergence | Helped |
| Use diminishing step sizes with inconsistent reads and writes, without bounded-gradient assumptions | Hogwild! · Strongly convex stochastic optimization | expected squared distance to optimum: O(1/t) | Helped |
| Use a position-based update that randomly selects one nonzero gradient coordinate | General Hogwild! recursion · Convergence bound per single vector-entry update | expected squared distance to optimum | Helped |
| Increase the delay to τ ∈ {1, 10, 100} while updating the whole nonzero gradient support | Hogwild! general recursion · ijcnn1 and covtype | training loss: τ ∈ {1, 10, 100} | No clear effect |
| Use smaller fractions of the nonzero gradient support per update | Hogwild! general recursion · ijcnn1 and covtype | training loss: v∈{1,3/4,2/3,1/2,1/3, 1/4} | Mixed |
| Drop convexity of individual component functions while retaining smoothness and strong convexity of the objective (ablation) | SGD and Hogwild! analysis · Strongly convex stochastic optimization | allowable initial step size: η_0 = \frac{1}{2 L} ... η_0 = \frac{1}{2 L\kappa} | Hurt |
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