Revisiting Estimation Bias in Policy Gradients for Deep Reinforcement Learning
This work addresses a theoretical issue in policy gradient methods for deep reinforcement learning, providing practical insights for improving algorithm stability, though it is incremental as it extends prior analysis to parameterized policies.
The paper tackles the problem of estimation bias in policy gradients for deep reinforcement learning, specifically due to state distribution shift, and shows that this bias can be reduced using small learning rates, adaptive optimizers, or KL regularization, with experimental validation on continuous control tasks.
We revisit the estimation bias in policy gradients for the discounted episodic Markov decision process (MDP) from Deep Reinforcement Learning (DRL) perspective. The objective is formulated theoretically as the expected returns discounted over the time horizon. One of the major policy gradient biases is the state distribution shift: the state distribution used to estimate the gradients differs from the theoretical formulation in that it does not take into account the discount factor. Existing discussion of the influence of this bias was limited to the tabular and softmax cases in the literature. Therefore, in this paper, we extend it to the DRL setting where the policy is parameterized and demonstrate how this bias can lead to suboptimal policies theoretically. We then discuss why the empirically inaccurate implementations with shifted state distribution can still be effective. We show that, despite such state distribution shift, the policy gradient estimation bias can be reduced in the following three ways: 1) a small learning rate; 2) an adaptive-learning-rate-based optimizer; and 3) KL regularization. Specifically, we show that a smaller learning rate, or, an adaptive learning rate, such as that used by Adam and RSMProp optimizers, makes the policy optimization robust to the bias. We further draw connections between optimizers and the optimization regularization to show that both the KL and the reverse KL regularization can significantly rectify this bias. Moreover, we provide extensive experiments on continuous control tasks to support our analysis. Our paper sheds light on how successful PG algorithms optimize policies in the DRL setting, and contributes insights into the practical issues in DRL.