Minimax weight and q-function learning for off-policy evaluation

We provide theoretical investigations into offpolicy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-Action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et al., 2018). (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can be combined with MWL in a doubly robust manner. (3) Several additional results that offer further insights, including the sample complexities of MWL and MQL, their asymptotic optimality in the tabular setting, how the learned importance weights depend the choice of the discriminator class, and how our methods provide a unified view of some old and new algorithms in RL.