DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning

In reinforcement learning (RL), temporal difference (TD) error is known to be related to the firing rate of dopamine neurons. It has been observed that each dopamine neuron does not behave uniformly, but each responds to the TD error in an optimistic or pessimistic manner, interpreted as a kind of distributional RL. To explain such biological data, a heuristic model has also been introduced with learning rates asymmetric for the positive and negative TD errors. However, this heuristic model is not theoretically grounded, and it is unknown whether it can work as an RL algorithm. This letter therefore introduces a novel theoretically grounded model with optimism and pessimism, which is derived from control as inference. In combination with ensemble learning, a distributional value function as a critic is estimated from regularly introduced optimism and pessimism. Based on its central value, a policy in an actor is improved. This proposed algorithm, so-called DROP (distributional and regular optimism and pessimism), is compared on dynamic tasks. Although the heuristic model showed poor learning performance, DROP demonstrated excellent performance in all tasks with high generality. In addition, DROP achieved learning performance comparable to the state-of-the-art algorithms. In other words, it was suggested that DROP is a new model that can elicit the potential contributions of optimism and pessimism.