Definition and Complexity of Some Basic Metareasoning Problems

TL;DR

This paper investigates the computational complexity of various fundamental metareasoning problems, establishing that they are generally NP-hard or PSPACE-hard, which highlights the inherent difficulty of optimal decision-making under resource constraints.

Contribution

It provides the first theoretical complexity results for key metareasoning problems, demonstrating their NP-hardness and PSPACE-hardness in realistic settings.

Findings

Deciding time allocation across algorithms is NP-complete.

Resource allocation among actions is NP-hard even with simple evaluations.

Choosing limited actions for disambiguation is NP-hard and PSPACE-hard.

Abstract

In most real-world settings, due to limited time or other resources, an agent cannot perform all potentially useful deliberation and information gathering actions. This leads to the metareasoning problem of selecting such actions. Decision-theoretic methods for metareasoning have been studied in AI, but there are few theoretical results on the complexity of metareasoning. We derive hardness results for three settings which most real metareasoning systems would have to encompass as special cases. In the first, the agent has to decide how to allocate its deliberation time across anytime algorithms running on different problem instances. We show this to be $\mathcal{NP}$-complete. In the second, the agent has to (dynamically) allocate its deliberation or information gathering resources across multiple actions that it has to choose among. We show this to be $\mathcal{NP}$-hard even when evaluating each individual action is extremely simple. In the third, the agent has to (dynamically) choose a limited number of deliberation or information gathering actions to disambiguate the state of the world. We show that this is $\mathcal{NP}$-hard under a natural restriction, and $\mathcal{PSPACE}$-hard in general.