Despite the wealth of research into provably efficient reinforcement learning algorithms, most works focus on tabular representation and thus struggle to handle exponentially or infinitely large state-action spaces. In this paper, we consider episodic reinforcement learning with a continuous state-action space which is assumed to be equipped with a natural metric that characterizes the proximity between different states and actions. We propose ZOOMRL, an online algorithm that leverages ideas from continuous bandits to learn an adaptive discretization of the joint space by zooming in more promising and frequently visited regions while carefully balancing the exploitationexploration trade-off. We show that ZOOMRL achieves a worst-case regret O(H) where H is the planning horizon, K is the number of episodes and d is the covering dimension of the space with respect to the metric. Moreover, our algorithm enjoys improved metric-dependent guarantees that reflect the geometry of the underlying space. Finally, we show that our algorithm is robust to small misspecification errors.
This paper provides an empirical evaluation of recently developed exploration algorithms within the Arcade Learning Environment (ALE). We study the use of different reward bonuses that incentives exploration in reinforcement learning. We do so by fixing the learning algorithm used and focusing only on the impact of the different exploration bonuses in the agent's performance. We use Rainbow, the state-of-the-art algorithm for value-based agents, and focus on some of the bonuses proposed in the last few years. We consider the impact these algorithms have on performance within the popular game MON-TEZUMA'S REVENGE which has gathered a lot of interest from the exploration community, across the the set of seven games identified by Bellemare et al. (2016) as challenging for exploration, and easier games where exploration is not an issue. We find that, in our setting, recently developed bonuses do not provide significantly improved performance on MONTEZUMA'S REVENGE or hard exploration games. We also find that existing bonus-based methods may negatively impact performance on games in which exploration is not an issue and may even perform worse than -greedy exploration.
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