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Reparameterization (RP) and likelihood ratio (LR) gradient estimators areused throughout machine and reinforcement learning; however, they are usuallyexplained as simple mathematical tricks without providing any insight intotheir nature. We use a first principles approach to explain LR and RP, and showa connection between the two via the divergence theorem. The theory motivatedus to derive optimal importance sampling schemes to reduce LR gradientvariance. Our newly derived distributions have analytic probability densitiesand can be directly sampled from. The improvement for Gaussian targetdistributions was modest, but for other distributions such as a Betadistribution, our method could lead to arbitrarily large improvements, and wascrucial to obtain competitive performance in evolution strategies experiments.

A unified view of likelihood ratio and reparameterization gradients and an optimal importance sampling scheme