Structured Monte Carlo Sampling for Nonisotropic Distributions via Determinantal Point Processes
This addresses sampling challenges in optimization and reinforcement learning, offering incremental improvements to existing methods.
The authors tackled the problem of Monte Carlo sampling for high-dimensional nonisotropic distributions by proposing DPPMC, a method using determinantal point processes to generate correlated samples that reduce estimator variance, and applied it to improve state-of-the-art in guided evolution strategies, CMA-ES, and trust region algorithms for optimization.
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.