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
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 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
NP-hard under a natural restriction, and PSPACE-hard in
general