Marginal Policy Gradients: A Unified Family of Estimators for Bounded Action Spaces with Applications

Abstract

Many complex domains, such as robotics control and real-time strategy (RTS) games, require an agent to learn a continuous control. In the former, an agent learns a policy over $\mathbb{R}^d$ and in the latter, over a discrete set of actions each of which is parametrized by a continuous parameter. Such problems are naturally solved using policy based reinforcement learning (RL) methods, but unfortunately these often suffer from high variance leading to instability and slow convergence. We show that in many cases a substantial portion of the variance in policy gradient estimators is completely unnecessary and can be eliminated without introducing bias. Unnecessary variance is introduced whenever policies over bounded action spaces are modeled using distributions with unbounded support, by applying a transformation T to the sampled action before execution in the environment. Recent works have studied variance reduced policy gradients for actions in bounded intervals, but to date no variance reduced methods exist when the action is a direction – constrained to the unit sphere – something often seen in RTS games. To address these challenges we: (1) introduce a stochastic policy gradient method for directional control; (2) introduce the marginal policy gradient framework, a powerful technique to obtain variance reduced policy gradients for arbitrary $T$; (3) show that marginal policy gradients are guaranteed to reduce variance, quantifying that reduction exactly; (4) validate our framework by applying the methods to a popular RTS game and a navigation task, demonstrating improvement over a policy gradient baseline.