LMC-SPSA, using two noisy function evaluations per iteration, is claimed to converge in W2 distance with an O(p^2) dimension bound and O(p/epsilon^2 + delta^2 p^3/epsilon^3) oracle complexity.
Particle Markov chain Monte Carlo methods,
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Zeroth-Order Langevin Monte Carlo via SPSA under Noisy Function Measurements
LMC-SPSA, using two noisy function evaluations per iteration, is claimed to converge in W2 distance with an O(p^2) dimension bound and O(p/epsilon^2 + delta^2 p^3/epsilon^3) oracle complexity.