  We study the variance of stochastic policy gradients (SPGs) with many action
samples per state. We derive a many-actions optimality condition, which
determines when many-actions SPG yields lower variance as compared to a
single-action agent with proportionally extended trajectory. We propose
Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for
many-actions sampling in the context of SPG. MBMA addresses issues associated
with existing implementations of many-actions SPG and yields lower bias and
comparable variance to SPG estimated from states in model-simulated rollouts.
We find that MBMA bias and variance structure matches that predicted by theory.
As a result, MBMA achieves improved sample efficiency and higher returns on a
range of continuous action environments as compared to model-free,
many-actions, and model-based on-policy SPG baselines.
