A Variant of the Wang-Foster-Kakade Lower Bound for the Discounted Setting

Recently, Wang et al. (2020) showed a highly intriguing hardness result for batch reinforcement learning (RL) with linearly realizable value function and good feature coverage in the finite-horizon case. In this note we show that once adapted to the discounted setting, the construction can be simplified to a 2-state MDP with 1-dimensional features, such that learning is impossible even with an infinite amount of data. Wang et al. (2020) recently showed that in finite-horizon batch RL, the sample complexity of evaluating a given policy π has an information-theoretic lower bound that is exponential in the horizon, even if realizable linear features are given (i.e., ϕ: S A R