Evaluating the Effectiveness of Index-Based Treatment Allocation

When resources are scarce, an allocation policy is needed to decide who receives a resource. This problem occurs, for instance, when allocating scarce medical resources and is often solved using modern ML methods. This paper introduces methods to evaluate index-based allocation policies -- that allocate a fixed number of resources to those who need them the most -- by using data from a randomized control trial. Such policies create dependencies between agents, which render the assumptions behind standard statistical tests invalid and limit the effectiveness of estimators. Addressing these challenges, we translate and extend recent ideas from the statistics literature to present an efficient estimator and methods for computing asymptotically correct confidence intervals. This enables us to effectively draw valid statistical conclusions, a critical gap in previous work. Our extensive experiments validate our methodology in practical settings, while also showcasing its statistical power. We conclude by proposing and empirically verifying extensions of our methodology that enable us to reevaluate a past randomized control trial to evaluate different ML allocation policies in the context of a mHealth program, drawing previously invisible conclusions.

A Spectral Approach to Off-Policy Evaluation for POMDPs

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes, where the evaluation policy depends only on observable variables but the behavior policy depends on latent states (Tennenholtz et al. (2020a)). Prior work on this problem uses a causal identification strategy based on one-step observable proxies of the hidden state, which relies on the invertibility of certain one-step moment matrices. In this work, we relax this requirement by using spectral methods and extending one-step proxies both into the past and future. We empirically compare our OPE methods to existing ones and demonstrate their improved prediction accuracy and greater generality. Lastly, we derive a separate Importance Sampling (IS) algorithm which relies on rank, distinctness, and positivity conditions, and not on the strict sufficiency conditions of observable trajectories with respect to the reward and hidden-state structure required by Tennenholtz et al. (2020a).

PAC Bounds for Imitation and Model-based Batch Learning of Contextual Markov Decision Processes

We consider the problem of batch multi-task reinforcement learning with observed context descriptors, motivated by its application to personalized medical treatment. In particular, we study two general classes of learning algorithms: direct policy learning (DPL), an imitation-learning based approach which learns from expert trajectories, and model-based learning. First, we derive sample complexity bounds for DPL, and then show that model-based learning from expert actions can, even with a finite model class, be impossible. After relaxing the conditions under which the model-based approach is expected to learn by allowing for greater coverage of state-action space, we provide sample complexity bounds for model-based learning with finite model classes, showing that there exist model classes with sample complexity exponential in their statistical complexity. We then derive a sample complexity upper bound for model-based learning based on a measure of concentration of the data distribution. Our results give formal justification for imitation learning over model-based learning in this setting.