Sparse reward environments are known to be challenging for reinforcement learning agents. In such environments, efficient and scalable exploration is crucial. Exploration is a means by which an agent gains information about the environment. We expand on this topic and propose a new intrinsic reward that systemically quantifies exploratory behavior and promotes state coverage by maximizing the information content of a trajectory taken by an agent. We compare our method to alternative exploration based intrinsic reward techniques, namely Curiosity Driven Learning and Random Network Distillation. We show that our information theoretic reward induces efficient exploration and outperforms in various games, including Montezuma Revenge, a known difficult task for reinforcement learning. Finally, we propose an extension that maximizes information content in a discretely compressed latent space which boosts sample efficiency and generalizes to continuous state spaces.

The branching factor of a game is the average number of new states reachable from a given state. It is a widely used metric in AI research on board games, but less often computed or discussed for videogames. This paper provides estimates for the branching factors of 103 Atari 2600 games, as implemented in the Arcade Learning Environment (ALE). Depending on the game, ALE exposes between 3 and 18 available actions per frame of gameplay, which is an upper bound on branching factor. This paper shows, based on an enumeration of the first 1 million distinct states reachable in each game, that the average branching factor is usually much lower, in many games barely above 1. In addition to reporting the branching factors, this paper aims to clarify what constitutes a distinct state in ALE.

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult case of strictly asymptotic synchronization is treated in a sequel. In both cases, we find that an observer, on average, will synchronize to the source state exponentially fast and that, as a result, the average accuracy in an observer's predictions of the source output approaches its optimal level exponentially fast as well. Additionally, we show here how to analytically calculate the synchronization rate for exact epsilon-machines and provide an efficient polynomial-time algorithm to test epsilon-machines for exactness.