Online Reinforcement Learning with Uncertain Episode Lengths
This addresses a limitation in episodic RL for scenarios with variable episode durations, such as robotics or gaming, though it is an incremental extension of existing frameworks.
The paper tackles the problem of episodic reinforcement learning where episode lengths are uncertain and drawn from a distribution, showing it is equivalent to online RL with general discounting. They design an algorithm that minimizes regret in this setting, achieving similar bounds even when the distribution is unknown, and demonstrate performance in a grid-world environment.
Existing episodic reinforcement algorithms assume that the length of an episode is fixed across time and known a priori. In this paper, we consider a general framework of episodic reinforcement learning when the length of each episode is drawn from a distribution. We first establish that this problem is equivalent to online reinforcement learning with general discounting where the learner is trying to optimize the expected discounted sum of rewards over an infinite horizon, but where the discounting function is not necessarily geometric. We show that minimizing regret with this new general discounting is equivalent to minimizing regret with uncertain episode lengths. We then design a reinforcement learning algorithm that minimizes regret with general discounting but acts for the setting with uncertain episode lengths. We instantiate our general bound for different types of discounting, including geometric and polynomial discounting. We also show that we can obtain similar regret bounds even when the uncertainty over the episode lengths is unknown, by estimating the unknown distribution over time. Finally, we compare our learning algorithms with existing value-iteration based episodic RL algorithms in a grid-world environment.