The efficient use of limited computational resources is an essential ingredient of intelligence. Selecting computations optimally according to rational metareasoning would achieve this, but this is computationally intractable. Inspired by psychology and neuroscience, we propose the first concrete and domain-general learning algorithm for approximating the optimal selection of computations: Bayesian metalevel policy search (BMPS). We derive this general, sample-efficient search algorithm for a computation-selecting metalevel policy based on the insight that the value of information lies between the myopic value of information and the value of perfect information. We evaluate BMPS on three increasingly difficult metareasoning problems: when to terminate computation, how to allocate computation between competing options, and planning. Across all three domains, BMPS achieved near-optimal performance and compared favorably to previously proposed metareasoning heuristics. Finally, we demonstrate the practical utility of BMPS in an emergency management scenario, even accounting for the overhead of metareasoning.

The conventional model for online planning under uncertainty assumes that an agent can stop and plan without incurring costs for the time spent planning. However, planning time is not free in most real-world settings. For example, an autonomous drone is subject to nature's forces, like gravity, even while it thinks, and must either pay a price for counteracting these forces to stay in place, or grapple with the state change caused by acquiescing to them. Policy optimization in these settings requires metareasoning---a process that trades off the cost of planning and the potential policy improvement that can be achieved. We formalize and analyze the metareasoning problem for Markov Decision Processes (MDPs). Our work subsumes previously studied special cases of metareasoning and shows that in the general case, metareasoning is at most polynomially harder than solving MDPs with any given algorithm that disregards the cost of thinking. For reasons we discuss, optimal general metareasoning turns out to be impractical, motivating approximations. We present approximate metareasoning procedures which rely on special properties of the BRTDP planning algorithm and explore the effectiveness of our methods on a variety of problems.

We can achieve significant gains in the value of computation by metareasoning about the nature or extent of base-level problem solving before executing a solution. However, resources that are irrevocably committed to metareasoning are not available for executing a solution. Thus, it is important to determine the portion of resources we wish to apply to metareasoning and control versus to the execution of a solution plan. Recent research on rational agency has highlighted the importance of limiting the consumption of resources by metareasoning machinery. We shall introduce the metareasoning-partition problem--the problem of ideally apportioning costly reasoning resources to planning a solution versus applying resource to executing a solution to a problem. We exercise prototypical metareasoning-partition models to probe the relationships between time allocated to metareasoning and to execution for different problem classes. Finally, we examine the value of metareasoning in the context of our functional analyses. This work was supported by a NASA Fellowship under Grant NCC-220-51, by the National Science Foundation under Grant IRI-8703710, and by the U.S. Army Research Office under Grant P-25514-EL. Computing facilities were provided by the SUMEX-AIM Resource under NLM Grant LM05208.

Selecting the right algorithm is an important problem in computer science, because the algorithm often has to exploit the structure of the input to be efficient. The human mind faces the same challenge. Therefore, solutions to the algorithm selection problem can inspire models of human strategy selection and vice versa. Here, we view the algorithm selection problem as a special case of metareasoning and derive a solution that outperforms existing methods in sorting algorithm selection. We apply our theory to model how people choose between cognitive strategies and test its prediction in a behavioral experiment. We find that people quickly learn to adaptively choose between cognitive strategies. People's choices in our experiment are consistent with our model but inconsistent with previous theories of human strategy selection. Rational metareasoning appears to be a promising framework for reverse-engineering how people choose among cognitive strategies and translating the results into better solutions to the algorithm selection problem.

The notion of bounded rationality originated from the insight that perfectly rational behavior cannot be realized by agents with limited cognitive or computational resources. Research on bounded rationality, mainly initiated by Herbert Simon, has a longstanding tradition in economics and the social sciences, but also plays a major role in modern AI and intelligent agent design. Taking actions under bounded resources requires an agent to reflect on how to use these resources in an optimal way - hence, to reason and make decisions on a meta-level. In this paper, we will look at automated machine learning (AutoML) and related problems from the perspective of bounded rationality, essentially viewing an AutoML tool as an agent that has to train a model on a given set of data, and the search for a good way of doing so (a suitable "ML pipeline") as deliberation on a meta-level.