Clinical Online Recommendation with Subgroup Rank Feedback

Many real applications in experimental design need to make decisions online. Each decision leads to a stochastic reward with initially unknown distribution. New decisions are made based on the observations of previous rewards. To maximize the total reward, one needs to solve the tradeoff between exploring different strategies and exploiting currently optimal strategies. This kind of tradeoff problems can be formalized as Multi-armed bandit problem. We recommend strategies in series and generate new recommendations based on noisy rewards of previous strategies. When the reward for a strategy is difficult to quantify, classical bandit algorithms are no longer optimal. This paper, studies the Multi-armed bandit problem with feedback given as a stochastic rank list instead of quantified reward values. We propose an algorithm for this new problem and show its optimality. A real application of this algorithm on clinical treatment is helping paralyzed patient to regain the ability to stand on their own feet.