Problem Solving as Probabilistic Inference with Subgoaling: Explaining Human Successes and Pitfalls in the Tower of Hanoi

How do humans and other animals face novel problems for which predefined solutions are not available? Human problem solving links to flexible reasoning and inference rather than to slow trial-and-error learning. It has received considerable attention since the early days of cognitive science, giving rise to well known cognitive architectures such as SOAR and ACT-R, but its computational and brain mechanisms remain incompletely known. Furthermore, it is still unclear whether problem solving is a “specialized” domain or module of cognition, in the sense that it requires computations that are fundamentally different from those supporting perception and action systems. Here we advance a novel view of human problem solving as probabilistic inference with subgoaling. In this perspective, key insights from cognitive architectures are retained such as the importance of using subgoals to split problems into subproblems. However, here the underlying computations use probabilistic inference methods analogous to those that are increasingly popular in the study of perception and action systems. To test our model we focus on the widely used Tower of Hanoi (ToH) task, and show that our proposed method can reproduce characteristic idiosyncrasies of human problem solvers: their sensitivity to the “community structure” of the ToH and their difficulties in executing so-called “counterintuitive” movements. Our analysis reveals that subgoals have two key roles in probabilistic inference and problem solving. First, prior beliefs on (likely) useful subgoals carve the problem space and define an implicit metric for the problem at hand—a metric to which humans are sensitive. Second, subgoals are used as waypoints in the probabilistic problem solving inference and permit to find effective solutions that, when unavailable, lead to problem solving deficits. Our study thus suggests that a probabilistic inference scheme enhanced with subgoals provides a comprehensive framework to study problem solving and its deficits.Author Summary: How humans solve challenging problems such as the Tower of Hanoi (ToH) or related puzzles is still largely unknown. Here we advance a computational model that uses the same probabilistic inference methods as those that are increasingly popular in the study of perception and action systems, thus making the point that problem solving does not need to be a specialized module or domain of cognition, but it can use the same computations underlying sensorimotor behavior. Crucially, we augment the probabilistic inference methods with subgoaling mechanisms that essentially permit to split the problem space into more manageable subparts, which are easier to solve. We show that our computational model can correctly reproduce important characteristics (and pitfalls) of human problem solving, including the sensitivity to the “community structure” of the ToH and the difficulty of executing so-called “counterintuitive” movements that require to (temporarily) move away from the final goal to successively achieve it.