Generalized Bandits with Learning and Queueing in Split Liver Transplantation

Abstract

Split liver transplantation (SLT) is a procedure that tries to save two lives by dividing one donor liver and transplanting the sections into two recipients. Despite SLT's potential to relieve the acute shortage of donated livers in the US, it is rarely used, in part because few surgeons in the US have learned to perform SLT. One barrier for young surgeons to acquire the skills to perform SLT is the need to perform actual SLT surgeries to become proficient, and the lower success rate such early surgeries have. Further, because SLT is a delicate operation, even with practice, some medical teams may still have only mixed success. This paper studies the donated liver allocation problem in a setting where surgeons with different potential abilities may learn SLT, becoming skilled over time. We formulate a multi-armed bandit (MAB) model, in which learning curves are embedded in the reward functions, to address the trade-off between discovering and developing talents (exploration) and utilizing a defined group of already-skilled surgeons (exploitation). To solve our MAB learning model, we propose the L-UCB, FL-UCB, and QFL-UCB algorithms, all variants of the upper confidence bound (UCB) algorithm, enhanced with additional features such as learning, fairness, queueing dynamics, and arm dependence. We prove that the regrets of our algorithms, that is, the loss in total rewards due to lack of information about surgeons' aptitudes, are bounded by O(log t). We also show they have superior numerical performance compared to standard bandit algorithms in settings where learning exists. From an application standpoint, our results provide insights into 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.