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.
If a smooth function is globally P L and coercive, then it has a unique minimizer.https://www.racetothebottom.xyz/posts/PL-smooth-unique/, 2025
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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.