  Being able to reason in an environment with a large number of discrete
actions is essential to bringing reinforcement learning to a larger class of
problems. Recommender systems, industrial plants and language models are only
some of the many real-world tasks involving large numbers of discrete actions
for which current methods are difficult or even often impossible to apply. An
ability to generalize over the set of actions as well as sub-linear complexity
relative to the size of the set are both necessary to handle such tasks.
Current approaches are not able to provide both of these, which motivates the
work in this paper. Our proposed approach leverages prior information about the
actions to embed them in a continuous space upon which it can generalize.
Additionally, approximate nearest-neighbor methods allow for logarithmic-time
lookup complexity relative to the number of actions, which is necessary for
time-wise tractable training. This combined approach allows reinforcement
learning methods to be applied to large-scale learning problems previously
intractable with current methods. We demonstrate our algorithm's abilities on a
series of tasks having up to one million actions.
