Planning under Distribution Shifts with Causal POMDPs

TL;DR

This paper introduces a causal POMDP framework that models environment shifts as interventions, enabling robust planning under distribution changes while preserving computational tractability.

Contribution

It formulates a causal POMDP approach that accounts for distribution shifts as interventions, maintaining PWLC properties for effective planning.

Findings

Framework models shifts as interventions on causal POMDPs

Belief updates include latent state and domain changes

Value function remains PWLC under distribution shifts

Abstract

In the real world, planning is often challenged by distribution shifts. As such, a model of the environment obtained under one set of conditions may no longer remain valid as the distribution of states or the environment dynamics change, which in turn causes previously learned strategies to fail. In this work, we propose a theoretical framework for planning under partial observability using Partially Observable Markov Decision Processes (POMDPs) formulated using causal knowledge. By representing shifts in the environment as interventions on this causal POMDP, the framework enables evaluating plans under hypothesized changes and actively identifying which components of the environment have been altered. We show how to maintain and update a belief over both the latent state and the underlying domain, and we prove that the value function remains piecewise linear and convex (PWLC) in this augmented belief space. Preservation of PWLC under distribution shifts has the advantage of maintaining the tractability of planning via $\alpha$-vector-based POMDP methods.