Under the local PL condition with multiplicative noise for C² functions, (S)GD asymptotic rates match those of strongly convex quadratics via a geometric argument.
Polyak’s heavy ball method achieves accelerated local rate of convergence under Polyak-Lojasiewicz inequality.arXiv preprint arXiv:2410.16849, 2024
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Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach
Under the local PL condition with multiplicative noise for C² functions, (S)GD asymptotic rates match those of strongly convex quadratics via a geometric argument.