I want to train a DQN model in an off-policy fashion, where my behavior policy is an older agent. I have a big memory of a lot of episodes of this agent. Now I want to find a better policy using DQN. Now I am just wondering, in the "normal" DQN case you would use the experience replay buffer and would update behavior and target policy online (behavior not really online but with the time lag introduced after which these parameters are also updated).
In my case, I already have all the experience and would like to learn from it. Do you think it makes sense to use the exact same procedure in this context, so sampling one new action, state and immediate reward, follow up action or could it be better here to use the fact that all experience is already stored to exchange $R_{t+1} + \gamma \max Q(S_{t+1},a)$ with some more future information about the rewards (up to the point of Monte Carlo where you take $G_t$ so the discounted cumulative reward seen during the episode from point t onwards)?