  Motivated by the importance of explainability in modern machine learning, we
design bandit algorithms that are efficient and interpretable. A bandit
algorithm is interpretable if it explores with the objective of reducing
uncertainty in the unknown model parameter. To quantify the interpretability,
we introduce a novel metric of model error, which compares the rate reduction
of the mean reward estimates to their actual means among all the plausible
actions. We propose CODE, a bandit algorithm based on a Constrained Optimal
DEsign, that is interpretable and maximally reduces the uncertainty. The key
idea in CODE is to explore among all plausible actions, determined by a
statistical constraint, to achieve interpretability. We implement CODE
efficiently in both multi-armed and linear bandits and derive near-optimal
regret bounds by leveraging the optimality criteria of the approximate optimal
design. CODE can be also viewed as removing phases in conventional phased
elimination, which makes it more practical and general. We demonstrate the
advantage of CODE by numerical experiments on both synthetic and real-world
problems. CODE outperforms other state-of-the-art interpretable designs while
matching the performance of popular but uninterpretable designs, such as upper
confidence bound algorithms.
