We use induction to prove this statement. The penultimate step follows from the induction hypothesis completing the proof. Then, the fixed point of Eq.(5) is the value function of in f M . We focus on permanent value function in the next two theorems. The permanent value function is updated using Eq.

Deep reinforcement learning (RL) has achieved remarkable successes in complex tasks, e.g Go [

Recent developments in reinforcement learning (RL) led to algorithms that surpass human experts in a broad range of tasks [Mnih et al., 2015, Vinyals et al., 2019, Schrittwieser et al., 2020, Wurman et al.,

HRL lead to improved sample complexity, and how much of an improvement can it provide? Theoretical work on sample-complexity bound in Machine Learning has been integral to the development of the field.

We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation.

Most existing methods explain why an agent takes individual actions rather than pinpointing the critical steps to its final reward.

However, existing offline RL methods tend to behave poorly during fine-tuning. In this paper, we study the fine-tuning problem in the context of conservative offline RL methods and we devise an approach for learning an effective initialization from offline data that also enables fast online fine-tuning capabilities.