Proficiency in many sophisticated tasks is attained through experience-based learning, in other words, learning by doing. For example, transplant surgeons need to practice difficult surgeries to actually master the skills required. Meanwhile, such experienced-based learning may affect other stakeholders, for example, patients eligible for transplant surgeries. In such a situation, a central planner may want to identify and develop surgeons with high aptitudes, while ensuring that patients still have excellent outcomes and equitable access to organs. To model such a situation, we formulate a multi-armed bandit (MAB) problem, in which parametric learning curves are embedded in the reward functions to capture experience-based learning. In addition, our model includes provisions ensuring that the choices of arms are subject to fairness constraints (ensuring equity), incorporates queueing dynamics (to capture waiting time dynamics), and arm dependence (to capture learning across similar surgeries). To solve our MAB problem, we propose the L-UCB, FL-UCB, and QFL-UCB algorithms, all variants of the upper confidence bound (UCB) algorithm that attain guaranteed performance on problems enhanced with experience-based learning, fairness, queueing dynamics, and arm dependence: We prove that the regrets of all of our algorithms are bounded by O(log t). We demonstrate our model and algorithms on the split liver transplantation (SLT) allocation problem; showing that our algorithms have superior numerical performance compared to standard bandit algorithms in settings where experience-based learning, fairness, queueing, and arm dependence exist. From an application standpoint, our algorithms could be applied to help evaluate potential strategies to increase the proliferation of SLT and other technically-difficult medical procedures. From a methodological point of view, our proposed MAB model and algorithms are generic and have broad application prospects
