Before revision:  This result implies the optimal sample complexity for offline learning and separates the local uniform OPE from the global case due to the extra S factor. Paramountly, the\tilde{O}\emph{  model-based method combining with our new analysis technique (singleton absorbing MDP) can be adapted to the new settings: offline task-agnostic and the offline reward-free with optimal complexity \tilde{O}(H^2\log(K)/d_m\epsilon^2) (K is the number of tasks) and \tilde{O}(H^2S/d_m\epsilon^2) respectively , which provides a unified framework for simultaneously solving different offline RL problems.
After revision:  Here d_m is the minimal marginal state-action probability. Critically, the highlight in achieving the optimal rate\tilde{O}\emph{ model-based method combining with our new analysis technique (singleton absorbing MDP) can be adapted to the new settings: offline task-agnostic and the offline reward-free with optimal complexity \tilde{O}(H^2\log(K)/d_m\epsilon^2) (K is the number of tasks) and \tilde{O}(H^2S/d_m\epsilon^2) respectively , which provides a unified framework for simultaneously solving different offline RL problems.