  Agents that learn to select optimal actions represent a prominent focus of
the sequential decision-making literature. In the face of a complex environment
or constraints on time and resources, however, aiming to synthesize such an
optimal policy can become infeasible. These scenarios give rise to an important
trade-off between the information an agent must acquire to learn and the
sub-optimality of the resulting policy. While an agent designer has a
preference for how this trade-off is resolved, existing approaches further
require that the designer translate these preferences into a fixed learning
target for the agent. In this work, leveraging rate-distortion theory, we
automate this process such that the designer need only express their
preferences via a single hyperparameter and the agent is endowed with the
ability to compute its own learning targets that best achieve the desired
trade-off. We establish a general bound on expected discounted regret for an
agent that decides what to learn in this manner along with computational
experiments that illustrate the expressiveness of designer preferences and even
show improvements over Thompson sampling in identifying an optimal policy.
