A Hybrid Stochastic Policy Gradient Algorithm for Reinforcement Learning
This work addresses the efficiency of policy optimization in reinforcement learning, particularly for constrained or regularized settings, though it is incremental as it builds on existing estimators.
The authors tackled the problem of high variance in policy gradient methods for reinforcement learning by proposing a hybrid stochastic policy gradient estimator, which combines REINFORCE and SARAH estimators to reduce variance while handling constraints, achieving a best-known trajectory complexity of O(ε^{-3}) for composite problems, outperforming existing methods like REINFORCE/GPOMDP and SVRPG in numerical evaluations.
We propose a novel hybrid stochastic policy gradient estimator by combining an unbiased policy gradient estimator, the REINFORCE estimator, with another biased one, an adapted SARAH estimator for policy optimization. The hybrid policy gradient estimator is shown to be biased, but has variance reduced property. Using this estimator, we develop a new Proximal Hybrid Stochastic Policy Gradient Algorithm (ProxHSPGA) to solve a composite policy optimization problem that allows us to handle constraints or regularizers on the policy parameters. We first propose a single-looped algorithm then introduce a more practical restarting variant. We prove that both algorithms can achieve the best-known trajectory complexity $\mathcal{O}\left(\varepsilon^{-3}\right)$ to attain a first-order stationary point for the composite problem which is better than existing REINFORCE/GPOMDP $\mathcal{O}\left(\varepsilon^{-4}\right)$ and SVRPG $\mathcal{O}\left(\varepsilon^{-10/3}\right)$ in the non-composite setting. We evaluate the performance of our algorithm on several well-known examples in reinforcement learning. Numerical results show that our algorithm outperforms two existing methods on these examples. Moreover, the composite settings indeed have some advantages compared to the non-composite ones on certain problems.