A multilevel Monte Carlo gradient estimator inside stochastic gradient descent yields linear convergence claims and large speedups for PDE-constrained optimal control under uncertainty.
Projected stochastic gradients for convex constrained problems in Hilbert spaces,
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Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
A multilevel Monte Carlo gradient estimator inside stochastic gradient descent yields linear convergence claims and large speedups for PDE-constrained optimal control under uncertainty.