  Applying Q-learning to high-dimensional or continuous action spaces can be
difficult due to the required maximization over the set of possible actions.
Motivated by techniques from amortized inference, we replace the expensive
maximization over all actions with a maximization over a small subset of
possible actions sampled from a learned proposal distribution. The resulting
approach, which we dub Amortized Q-learning (AQL), is able to handle discrete,
continuous, or hybrid action spaces while maintaining the benefits of
Q-learning. Our experiments on continuous control tasks with up to 21
dimensional actions show that AQL outperforms D3PG (Barth-Maron et al, 2018)
and QT-Opt (Kalashnikov et al, 2018). Experiments on structured discrete action
spaces demonstrate that AQL can efficiently learn good policies in spaces with
thousands of discrete actions.
