Adaptive Order Q-learning

This paper revisits the estimation bias control problem of Q-learning, motivated by the fact that the estimation bias is not always evil, i.e., some environments benefit from overestimation bias or underestimation bias, while others suffer from these biases. Different from previous coarse-grained bias control methods, this paper proposes a fine-grained bias control algorithm called Order Q-learning. It uses the order statistic of multiple independent Q-tables to control bias and flexibly meet the personalized bias needs of different environments, i.e., the bias can vary from underestimation bias to overestimation bias as one selects a higher order Q-value. We derive the expected estimation bias and its lower bound and upper bound. They reveal that the expected estimation bias is inversely proportional to the number of Q-tables and proportional to the index of order statistic function. To show the versatility of Order Q-learning, we design an adaptive parameter adjustment strategy, leading to AdaOrder (Adaptive Order) Q-learning. It adaptively selects the number of Q-tables and the index of order statistic function via the number of visits to state-action pair and the average Q-value. We extend Order Q-learning and AdaOrder Q-learning to the large scale setting with function approximation, leading to Order DQN and AdaOrder DQN, respectively. Finally, we consider two experiment settings: deep reinforcement learning experiments show that our method outperforms several SOTA baselines drastically; tabular MDP experiments reveal fundamental insights into why our method can achieve superior performance.Our supplementary file can be found in https://1drv.ms/f/s!Atddp1iaDmL2gjv31CaGquw5WwYI.