This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from limited data (parametric uncertainty), while the second originates from the distribution of the returns (return uncertainty). We identify methods to learn these distributions with deep neural networks, where we estimate parametric uncertainty with Bayesian drop-out, while return uncertainty is propagated through the Bellman equation as a Gaussian distribution. Then, we identify that both can be jointly estimated in one network, which we call the Double Uncertain Value Network. The policy is directly derived from the learned distributions based on Thompson sampling. Experimental results show that both types of uncertainty may vastly improve learning in domains with a strong exploration challenge.
Efficient exploration in complex environments remains a major challenge for reinforcement learning. We propose bootstrapped DQN, a simple algorithm that explores in a computationally and statistically efficient manner through use of randomized value functions. Unlike dithering strategies such as epsilon-greedy exploration, bootstrapped DQN carries out temporally-extended (or deep) exploration; this can lead to exponentially faster learning. We demonstrate these benefits in complex stochastic MDPs and in the large-scale Arcade Learning Environment. Bootstrapped DQN substantially improves learning times and performance across most Atari games.