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

Understand

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.