Proceedings

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

Joshua Wendland, Markel Zubia, Roman Andriushchenko, Maris F. L. Galesloot, Milan Češka, Henrik von Kleist, Thiago D. Simão, Maximilian Weininger, Nils Jansen

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 6217-6226.

https://doi.org/10.24963/ijcai.2026/692

Keywords

  • Planning and Scheduling: POMDPs
  • Planning and Scheduling: Learning in planning and scheduling
  • Machine Learning: Partially observable reinforcement learning and POMDPs
  • Knowledge Representation and Reasoning: Causality

Abstract

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: (1) missing completely at random (MCAR), (2) missing at random (MAR), and (3) missing not at random (MNAR).

The problem is to compute near-optimal policies for a miss-MDP with an unknown missingness function, given a dataset of action-observation histories.

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 ε-optimal in the true miss-MDP.

Empirical results confirm the theory and demonstrate superior performance of our approach over two model-free methods.

Joshua Wendland, Markel Zubia, Roman Andriushchenko, Maris F. L. Galesloot, Milan Ceska, Henrik von Kleist, Thiago D. Simão, Maximilian Weininger, and Nils Jansen. 2026. Missingness-MDPs: Bridging the Theory of Missing Data and POMDPs. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 6217–6226. https://doi.org/10.24963/ijcai.2026/692
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