  We propose a new class of structured methods for Monte Carlo (MC) sampling,
called DPPMC, designed for high-dimensional nonisotropic distributions where
samples are correlated to reduce the variance of the estimator via
determinantal point processes. We successfully apply DPPMCs to problems
involving nonisotropic distributions arising in guided evolution strategy (GES)
methods for RL, CMA-ES techniques and trust region algorithms for blackbox
optimization, improving state-of-the-art in all these settings. In particular,
we show that DPPMCs drastically improve exploration profiles of the existing
evolution strategy algorithms. We further confirm our results, analyzing random
feature map estimators for Gaussian mixture kernels. We provide theoretical
justification of our empirical results, showing a connection between DPPMCs and
structured orthogonal MC methods for isotropic distributions.
