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Abstract When developing models in cognitive science, researchers typically start with their own intuitions about human behavior in a given task and then build in mechanisms that explain additional aspects of the data. This refinement step is often hindered by how difficult it is to distinguish the unpredictable randomness of people’s decisions from meaningful deviations between those decisions and the model. One solution for this problem is to compare the model against deep neural networks trained on behavioral data, which can detect almost any pattern given sufficient data. Here, we apply this method to the domain of planning with a heuristic search model for human play in 4-in-a-row, a combinatorial game where participants think multiple steps into the future. Using a data set consisting of 10,874,547 games, we train deep neural networks to predict human moves and find that they accurately do so while capturing meaningful patterns in the data. Thus, deviations between the model and the best network allow us to identify opportunities for model improvement despite starting with a model that has undergone substantial testing in previous work. Based on this analysis, we add three extensions to the model that range from a simple opening bias to specific adjustments regarding endgame planning. Overall, our work demonstrates the advantages of model comparison with a high-performance deep neural network as well as the feasibility of scaling cognitive models to massive data sets for systematically investigating the processes underlying human sequential decision-making. 

The introduction of large-scale data sets in psychology allows for more robust accounts of various cognitive mechanisms, one of which is human learning. However, these data sets provide participants with complete autonomy over their own participation in the task, and therefore require precisely studying the factors influencing dropout alongside learning. In this work, we present such a data set where 1,234,844 participants play 10,874,547 games of a challenging variant of tic-tac-toe. We establish that there is a correlation between task performance and total experience, and independently analyze participants’ dropout behavior and learning trajectories. We find evidence for stopping patterns as a function of playing strength and investigate the processes underlying playing strength increases with experience using a set of metrics derived from a planning model. Finally, we develop a joint model to account for both dropout and learning functions which replicates our empirical findings. 

Models in cognitive science are often restricted for the sake of interpretability, and as a result may miss patterns in the data that are instead classified as noise. In contrast, deep neural networks can detect almost any pattern given sufficient data, but have only recently been applied to large-scale data sets and tasks for which there already exist process-level models to compare against. Here, we train deep neural networks to predict human play in 4-in-a-row, a combinatorial game of intermediate complexity, using a data set of 10,874,547 games. We compare these networks to a planning model based on a heuristic function and tree search, and make suggestions for model improvements based on this analysis. This work provides the foundation for estimating a noise ceiling on massive data sets as well as systematically investigating the processes underlying human sequential decision-making. 

Planning, the process of evaluating the future consequences of actions, is typically formalized as search over a decision tree. This procedure increases expected rewards but is computationally expensive. Past attempts to understand how people mitigate the costs of planning have been guided by heuristics or the accumulation of prior experience, both of which are intractable in novel, high-complexity tasks. In this work, we propose a normative framework for optimizing the depth of tree search. Specifically, we model a metacognitive process via Bayesian inference to compute optimal planning depth. We show that our model makes sensible predictions over a range of parameters without relying on retrospection and that integrating past experiences into our model produces results that are consistent with the transition from goal-directed to habitual behavior over time and the uncertainty associated with prospective and retrospective estimates. Finally, we derive an online variant of our model that replicates these results.