Given M with (M) < 1andanunsatur (M)

Computing an approximately optimal policy with high probability in this case is known as PAC RL with a generative model.

Hence, a "fair" reward allocation scheme is desirable to give all parties enough incentives to join the collaboration.

Figure 11: Comparison of HCAM (labeled as HTM) with different chunk sizes to TrXL across the different ballet levels. The performance of the HCAM model is robust to varying chunk size, indicating that HCAM does not need a task-relevant segmentation to perform well.

Sample efficiencyof ESRL is independent of the chosen risk aversion threshold and quality of the behavior policy.

We introduce a method for learning provably stable deep neural network based dynamic models from observed data.

As our first contribution, we revisit recent FSIG works and their experiments.

Reward allocation, also known as the credit assignment problem, has been an important topic ineconomics, engineering, andmachine learning.

This is only for the ease of visualization. For linear MDP,In the generative model setting, Agarwal et al. [2020] shows model-based approach is still minimax optimal O((1 γ) 3SA/2)byusing as-absorbing MDP construction andthismodelbased technique is later reused for other more general settings (e.g. Itrequires high probability guarantee for learning optimal policyforany reward function, which is strictly stronger than the standard learning task that one only needs to learn to optimal policy for a fixed reward. B.2 GeneralabsorbingMDP The general absorbing MDP is defined as follows: for a fixed states and a sequence {ut}Ht=1, MDPMs,{ut}Ht=1 is identical toM for all states excepts, and state s is absorbing in the sense PMs,{ut}Ht=1(s|s,a) = 1 for all a, and the instantaneous reward at timet is rt(s,a) = ut for all a A. Also,weusetheshorthand notationVπ{s,ut} forVπs,Ms,{u We focus on the first claim. Later we shall remove the conditional onN (see SectionB.7). We use the singleton-absorbing MDPMs,{u?t}Ht=1 to handle the case (recallu?t

As inthe classical problem, weights are fixed by an adversary and elements appear in random order. In contrast to previous variants of predictions, our algorithm only has access toamuch weakerpiece ofinformation: anadditive gapc.