Greedy Approximation Algorithms for Active Sequential Hypothesis Testing

Abstract

In the problem of active sequential hypotheses testing (ASHT), a learner seeks to identify the true hypothesis ℎ * from among a set of hypotheses . The learner is given a set of actions and knows the outcome distribution of any action under any true hypothesis. While repeatedly playing the entire set of actions su ces to identify ℎ * , a cost is incurred with each action. Thus, given a target error > 0, the goal is to nd the minimal cost policy for sequentially selecting actions that identify ℎ * with probability at least 1 − .This paper provides the rst approximation algorithms for ASHT, under two types of adaptivity. First, a policy is partially adaptive if it xes a sequence of actions in advance and adaptively decides when to terminate and what hypothesis to return. Under partial adaptivity, we provide anwhere is a natural separation parameter between the hypotheses. Second, a policy is fully adaptive if action selection is allowed to depend on previous outcomes. Under full adaptivity, we provide an ( −1 log(| |/ ) log | |)-approximation algorithm. We numerically investigate the performance of our algorithms using both synthetic and real-world data, showing that our algorithms outperform a previously proposed heuristic policy.