Controlling underestimation bias in reinforcement learning via minmax operation

Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning. However, current methods that address the overestimation problem tend to introduce underestimation, which face a challenge of precise decision-making in many fields. To address this issue, we conduct a theoretical analysis of the underestimation bias and propose the minmax operation, which allow for flexible control of the estimation bias. Specifically, we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence. Then, a minimum value is selected to obtain more accurate value estimations. Moreover, based on the minmax operation, we propose two novel algorithms by combining Deep Q-Network (DQN) and Double DQN (DDQN), named minmax-DQN and minmax-DDQN. Meanwhile, we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation, which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation. Furthermore, the variance is also reduced, which is helpful to improve the network training stability. Finally, we conduct numerous comparative experiments in various environments, which empirically demonstrate the superiority of our method.