Efficient and Interpretable Bandit Algorithms

Motivated by the importance of explainability in modern machine learning, we design bandit algorithms that are \emph{efficient} and \emph{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 \textit{uncertainty loss}, which compares the rate of the uncertainty reduction to the theoretical optimum. We propose CODE, a bandit algorithm based on a \textbf{C}onstrained \textbf{O}ptimal \textbf{DE}sign, 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.