  Much of the recent literature on bandit learning focuses on algorithms that
aim to converge on an optimal action. One shortcoming is that this orientation
does not account for time sensitivity, which can play a crucial role when
learning an optimal action requires much more information than near-optimal
ones. Indeed, popular approaches such as upper-confidence-bound methods and
Thompson sampling can fare poorly in such situations. We consider instead
learning a satisficing action, which is near-optimal while requiring less
information, and propose satisficing Thompson sampling, an algorithm that
serves this purpose. We establish a general bound on expected discounted regret
and study the application of satisficing Thompson sampling to linear and
infinite-armed bandits, demonstrating arbitrarily large benefits over Thompson
sampling. We also discuss the relation between the notion of satisficing and
the theory of rate distortion, which offers guidance on the selection of
satisficing actions.
