On the Complexity Gap Between POMDPs and Multi-Environment POMDPs

Key points

• Multi-environment POMDPs (ME-POMDPs) generalize POMDPs by encoding a finite set of possible environments, capturing model uncertainty.1
• We expand the complexity landscape of ME-POMDPs by identifying which subclasses retain this $\mathsf{PSPACE}$-completeness.1
• We first prove the $\mathsf{NP}$-completeness of multi-environment blind MDPs and deterministic POMDPs using a certain closure-under-mixture condition.1
• Finally, we show existential theory of the reals ($\exists \mathbb{R}$)-completeness for numerous ME-POMDP problems under time-dependent Markovian policies or finite-state controllers that are $\mathsf{NP}$-complete for standard POMDPs.1

Sources (1)

• [1]On the Complexity Gap Between POMDPs and Multi-Environment POMDPs
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 10, 03:45 PM

  The finite-horizon robust reward maximization problem for a ME-POMDP asks for a policy that maximizes reward in the worst environment, and recent work has shown this problem to be $\mathsf{PSPACE}$-complete.

  Multi-environment POMDPs (ME-POMDPs) generalize POMDPs by encoding a finite set of possible environments, capturing model uncertainty.

Extractive summary: sentences quoted from the sources.