  Standard reinforcement learning (RL) aims to find an optimal policy that
identifies the best action for each state. However, in healthcare settings,
many actions may be near-equivalent with respect to the reward (e.g.,
survival). We consider an alternative objective -- learning set-valued policies
to capture near-equivalent actions that lead to similar cumulative rewards. We
propose a model-free algorithm based on temporal difference learning and a
near-greedy heuristic for action selection. We analyze the theoretical
properties of the proposed algorithm, providing optimality guarantees and
demonstrate our approach on simulated environments and a real clinical task.
Empirically, the proposed algorithm exhibits good convergence properties and
discovers meaningful near-equivalent actions. Our work provides theoretical, as
well as practical, foundations for clinician/human-in-the-loop decision making,
in which humans (e.g., clinicians, patients) can incorporate additional
knowledge (e.g., side effects, patient preference) when selecting among
near-equivalent actions.
