Missingness-MDPs: Bridging the Theory of Missing Data and POMDPs

We introduce missingness-MDPs (miss-MDPs), a novel subclass of partially observable Markov decision processes (POMDPs) that incorporates the theory of missing data. A miss-MDP is a POMDP whose observation function is a missingness function, specifying the probability that individual state features are missing (i.e., unobserved) at a time step. The literature distinguishes three canonical missingness types: missing (1) completely at random (MCAR), (2) at random (MAR), and (3) not at random (MNAR). Our planning problem is to compute near-optimal policies for a miss-MDP with an unknown missingness function, given a dataset of action-observation trajectories. Achieving such optimality guarantees for policies requires learning the missingness function from data, which is infeasible for general POMDPs. To overcome this challenge, we exploit the structural properties of different missingness types to derive probably approximately correct (PAC) algorithms for learning the missingness function. These algorithms yield an approximate but fully specified miss-MDP that we solve using off-the-shelf planning methods. We prove that, with high probability, the resulting policies are epsilon-optimal in the true miss-MDP. Empirical results confirm the theory and demonstrate superior performance of our approach over two model-free POMDP methods.

Evaluation of Active Feature Acquisition Methods for Static Feature Settings

Active feature acquisition (AFA) agents, crucial in domains like healthcare where acquiring features is often costly or harmful, determine the optimal set of features for a subsequent classification task. As deploying an AFA agent introduces a shift in missingness distribution, it's vital to assess its expected performance at deployment using retrospective data. In a companion paper, we introduce a semi-offline reinforcement learning (RL) framework for active feature acquisition performance evaluation (AFAPE) where features are assumed to be time-dependent. Here, we study and extend the AFAPE problem to cover static feature settings, where features are time-invariant, and hence provide more flexibility to the AFA agents in deciding the order of the acquisitions. In this static feature setting, we derive and adapt new inverse probability weighting (IPW), direct method (DM), and double reinforcement learning (DRL) estimators within the semi-offline RL framework. These estimators can be applied when the missingness in the retrospective dataset follows a missing-at-random (MAR) pattern. They also can be applied to missing-not-at-random (MNAR) patterns in conjunction with appropriate existing missing data techniques. We illustrate the improved data efficiency offered by the semi-offline RL estimators in synthetic and real-world data experiments under synthetic MAR and MNAR missingness.

Evaluation of Active Feature Acquisition Methods for Time-varying Feature Settings

Machine learning methods often assume input features are available at no cost. However, in domains like healthcare, where acquiring features could be expensive or harmful, it is necessary to balance a feature's acquisition cost against its predictive value. The task of training an AI agent to decide which features to acquire is called active feature acquisition (AFA). By deploying an AFA agent, we effectively alter the acquisition strategy and trigger a distribution shift. To safely deploy AFA agents under this distribution shift, we present the problem of active feature acquisition performance evaluation (AFAPE). We examine AFAPE under i) a no direct effect (NDE) assumption, stating that acquisitions don't affect the underlying feature values; and ii) a no unobserved confounding (NUC) assumption, stating that retrospective feature acquisition decisions were only based on observed features. We show that one can apply offline reinforcement learning under the NUC assumption and missing data methods under the NDE assumption. When NUC and NDE hold, we propose a novel semi-offline reinforcement learning framework, which requires a weaker positivity assumption and yields more data-efficient estimators. We introduce three novel estimators: a direct method (DM), an inverse probability weighting (IPW), and a double reinforcement learning (DRL) estimator.