Planning under Distribution Shifts with Causal POMDPs
This work addresses the problem of maintaining planning tractability for agents operating in environments with distribution shifts, which is crucial for real-world applications where environmental conditions can change.
This paper proposes a theoretical framework for planning under partial observability and distribution shifts using Causal Partially Observable Markov Decision Processes (Causal POMDPs). The framework allows for evaluating plans under hypothesized environmental changes and identifying altered components, while proving that the value function remains piecewise linear and convex (PWLC) in an augmented belief space.
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 $α$-vector-based POMDP methods.