Abstract
Making good decisions requires thinking ahead, but the huge number of actions and outcomes one could consider makes exhaustive planning infeasible for computationally constrained agents, such as humans. How people are nevertheless able to solve novel problems when their actions have long-reaching consequences is thus a long-standing question in cognitive science. To address this question, we propose a model of resource-constrained planning that allows us to derive optimal planning strategies. We find that previously proposed heuristics such as best-first search are near optimal under some circumstances but not others. In a mouse-tracking paradigm, we show that people adapt their planning strategies accordingly, planning in a manner that is broadly consistent with the optimal model but not with any single heuristic model. We also find systematic deviations from the optimal model that might result from additional cognitive constraints that are yet to be uncovered.
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Data availability
The anonymized data that support the findings of this study are available on the Open Science Framework (https://osf.io/6venh/).
Code availability
The modelling and analysis code is available on the Open Science Framework (https://osf.io/6venh/).
Change history
16 June 2022
A Correction to this paper has been published: https://doi.org/10.1038/s41562-022-01411-w
References
Huys, Q. J. M. et al. Interplay of approximate planning strategies. Proc. Natl Acad. Sci. USA 112, 3098–3103 (2015).
Huys, Q. J. M. et al. Bonsai trees in your head: how the Pavlovian system sculpts goal-directed choices by pruning decision trees. PLoS Comput. Biol. 8, e1002410 (2012).
van Opheusden, B., et al. Revealing the impact of expertise on human planning with a two-player board game. Preprint at PsyArXiv https://doi.org/10.31234/osf.io/rhq5j (2021).
MacGregor, J. N., Ormerod, T. C. & Chronicle, E. P. Information processing and insight: a process model of performance on the nine-dot and related problems. J. Exp. Psychol. Learn. Mem. Cogn. 27, 176–201 (2001).
Keramati, M., Smittenaar, P., Dolan, R. J. & Dayan, P. Adaptive integration of habits into depth-limited planning defines a habitual-goal–directed spectrum. Proc. Natl Acad. Sci. USA 113, 12868–12873 (2016).
Krusche, M. J. F., Schulz, E., Guez, A. & Speekenbrink, M. Adaptive planning in human search. Preprint at bioRxiv https://doi.org/10.1101/268938 (2018).
Snider, J., Lee, D., Poizner, H. & Gepshtein, S. Prospective optimization with limited resources. PLoS Comput. Biol. 11, e1004501 (2015).
Von Neumann, J. & Morgenstern, O. The Theory of Games and Economic Behavior (Princeton Univ. Press, 1944).
Stahl, D. O. & Wilson, P. W. Experimental evidence on players’ models of other players. J. Econ. Behav. Organ. 25, 309–327 (1994).
Camerer, C. F., Ho, T.-H. & Chong, J.-K. A cognitive hierarchy model of games. Q. J. Econ. 119, 861–898 (2004).
Newell, A. & Simon, H. The logic theory machine—a complex information processing system. IRE Trans. Inform. Theory 2, 61–79 (1956).
Griffiths, T. L. et al. Doing more with less: meta-reasoning and meta-learning in humans and machines. Curr. Opin. Behav. Sci. 29, 24–30 (2019).
Newell, A., Shaw, J. C. & Simon, H. A. Report on a general problem solving program. In Proc. International Conference on Information Processing 256–264 (UNESCO, Paris, 1959).
Newell, A. et al. Human Problem Solving Vol. 104 (Prentice-Hall, 1972).
Kool, W., Gershman, S. J. & Cushman, F. A. Cost–benefit arbitration between multiple reinforcement-learning systems. Psychol. Sci. 28, 1321–1333 (2017).
Norris, D. & Cutler, A. More why, less how: what we need from models of cognition. Cognition 213, 104688 (2021).
Marr, D. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (WH Freeman, 1982).
Anderson, J. R. The Adaptive Character of Thought (Psychology Press, 1990).
Savage, L. J. The Foundations of Statistics (John Wiley & Sons, 1954).
Tenenbaum, J. B. & Griffiths, T. L. Generalization, similarity and Bayesian inference. Behav. Brain Sci. 24, 629–640 (2001).
Anderson, J. R. The adaptive nature of human categorization. Psychol. Rev. 98, 409–429 (1991).
Ashby, F. G. & Alfonso-Reese, L. A. Categorization as probability density estimation. J. Math. Psychol. 39, 216–233 (1995).
Knill, D. C. & Richards, W. Perception as Bayesian Inference (Cambridge Univ. Press, 1996).
Oaksford, M. & Chater, N. A rational analysis of the selection task as optimal data selection. Psychol. Rev. 101, 608–631 (1994).
Gureckis, T. M. & Markant, D. B. Self-directed learning: a cognitive and computational perspective. Perspect. Psychol. Sci. 7, 464–481 (2012).
Howes, A., Lewis, R. L. & Vera, A. Rational adaptation under task and processing constraints: implications for testing theories of cognition and action. Psychol. Rev. 116, 717–751 (2009).
Lewis, R. L., Howes, A. & Singh, S. Computational rationality: linking mechanism and behavior through bounded utility maximization. Top. Cogn. Sci. 6, 279–311 (2014).
Gershman, S. J., Horvitz, E. J. & Tenenbaum, J. B. Computational rationality: a converging paradigm for intelligence in brains, minds, and machines. Science 349, 273–278 (2015).
Griffiths, T. L., Lieder, F. & Goodman, N. D. Rational use of cognitive resources: levels of analysis between the computational and the algorithmic. Top. Cogn. Sci. 7, 217–229 (2015).
Lieder, F. & Griffiths, T. L. Resource-rational analysis: understanding human cognition as the optimal use of limited computational resources. Behav. Brain Sci. 43, e1 (2020).
Simon, H. A. A behavioral model of rational choice. Q. J. Econ. 69, 99–118 (1955).
Bogacz, R., Brown, E., Moehlis, J., Holmes, P. & Cohen, J. D. The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychol. Rev. 113, 700–765 (2006).
Drugowitsch, J., Moreno-Bote, R., Churchland, A. K., Shadlen, M. N. & Pouget, A. The cost of accumulating evidence in perceptual decision making. J. Neurosci. 32, 3612–3628 (2012).
Tajima, S., Drugowitsch, J. & Pouget, A. Optimal policy for value-based decision-making. Nat. Commun. 7, 12400 (2016).
Tajima, S., Drugowitsch, J., Patel, N. & Pouget, A. Optimal policy for multi-alternative decisions. Nat. Neurosci. 22, 1503–1511 (2019).
Fudenberg, D., Strack, P. & Strzalecki, T. Speed, accuracy, and the optimal timing of choices. Am. Econ. Rev. 108, 3651–3684 (2018).
Callaway, F., Rangel, A. & Griffiths, T. L. Fixation patterns in simple choice reflect optimal information sampling. PLoS Comput. Biol. 17, e1008863 (2021).
Jang, A. I., Sharma, R. & Drugowitsch, J. Optimal policy for attention-modulated decisions explains human fixation behavior. eLife 10, e63436 (2021).
Sezener, C. E., Dezfouli, A. & Keramati, M. Optimizing the depth and the direction of prospective planning using information values. PLoS Comput. Biol. 15, e1006827 (2019).
Mattar, M. G. & Daw, N. D. Prioritized memory access explains planning and hippocampal replay. Nat. Neurosci. 21, 1609–1617 (2018).
Matheson, J. E. The economic value of analysis and computation. IEEE Trans. Syst. Sci. Cybern. 4, 325–332 (1968).
Horvitz, E. J. Reasoning about beliefs and actions under computational resource constraints. In Proc. 3rd Conference on Uncertainty in Artificial Intelligence (eds Kanal L. N. et al.) 429–447 (AUAI Press, 1987).
Russell, S. & Wefald, E. Principles of metareasoning. Artif. Intell. 49, 361–395 (1991).
Payne, J. W. Task complexity and contingent processing in decision making: an information search and protocol analysis. Organ. Behav. Hum. Perform. 16, 366–387 (1976).
Daw, N. D., Niv, Y. & Dayan, P. Uncertainty-based competition between prefrontal and dorsolateral striatal systems for behavioral control. Nat. Neurosci. 8, 1704–1711 (2005).
Keramati, M., Dezfouli, A. & Piray, P. Speed/accuracy trade-off between the habitual and the goal-directed processes. PLoS Comput. Biol. 7, e1002055 (2011).
Shenhav, A., Botvinick, M. & Cohen, J. The expected value of control: an integrative theory of anterior cingulate cortex function. Neuron 79, 217–240 (2013).
Kool, W. & Botvinick, M. Mental labour. Nat. Hum. Behav. 2, 899–908 (2018).
Hay, N., Russell, S., Tolpin, D. & Shimony, S. Selecting computations: theory and applications. In Proc. 28th Conference on Uncertainty in Artificial Intelligence (eds de Freitas, N. & Murphy, K.) 346–355 (AUAI Press, 2012).
Russell, S. J. & Norvig, P. Artificial Intelligence: A Modern Approach (Prentice Hall, 2002).
Solway, A. & Botvinick, M. M. Evidence integration in model-based tree search. Proc. Natl Acad. Sci. USA 112, 11708–11713 (2015).
De Groot, A. D. Thought and Choice in Chess (Grouton, 1965).
Chase, W. G. & Simon, H. A. Perception in chess. Cogn. Psychol. 4, 55–81 (1973).
Payne, J. W., Bettman, J. R. & Johnson, E. J. Adaptive strategy selection in decision making. J. Exp. Psychol. Learn. Mem. Cogn. 14, 534–552 (1988).
Ford, J. K., Schmitt, N., Schechtman, S. L., Hults, B. M. & Doherty, M. L. Process tracing methods: contributions, problems, and neglected research questions. Organ. Behav. Hum. Decis. Process. 43, 75–117 (1989).
Payne, J. W., Bettman, J. R. & Johnson, E. J. The Adaptive Decision Maker (Cambridge Univ. Press, 1993).
Gabaix, X., Laibson, D., Moloche, G. & Weinberg, S. Costly information acquisition: experimental analysis of a boundedly rational model. Am. Econ. Rev. 96, 1043–1068 (2006).
Schulte-Mecklenbeck, M., Kuehberger, A. & Johnson, J. G. in A Handbook of Process Tracing Methods for Decision Research (eds Schulte-Mecklenbeck, M. et al.) 37–58 (Psychology Press, 2011).
Ratcliff, R. & Smith, P. L. A comparison of sequential sampling models for two-choice reaction time. Psychol. Rev. 111, 333–367 (2004).
Teodorescu, A. R. & Usher, M. Disentangling decision models: from independence to competition. Psychol. Rev. 120, 1–38 (2013).
McMillen, T. & Holmes, P. The dynamics of choice among multiple alternatives. J. Math. Psychol. 50, 30–57 (2006).
Piantadosi, S. T. One parameter is always enough. AIP Adv. 8, 095118 (2018).
Sutton, R. S. Integrated architectures for learning, planning, and reacting based on approximating dynamic programming. In Proc. 7th International Conference on Machine Learning (eds Porter, B. & Mooney, R.) 216–224 (Morgan Kaumann, 1990).
Gigerenzer, G. Why heuristics work. Perspect. Psychol. Sci. 3, 20–29 (2008).
Gigerenzer, G. & Gaissmaier, W. Heuristic decision making. Annu. Rev. Psychol. 62, 451–482 (2011).
Todd, P. M. & Gigerenzer, G. Bounding rationality to the world. J. Econ. Psychol. 24, 143–165 (2003).
Gigerenzer, G. & Goldstein, D. G. Reasoning the fast and frugal way: models of bounded rationality. Psychol. Rev. 103, 650–659 (1996).
Gigerenzer, G. & Todd, P. M. Simple Heuristics That Make Us Smart (Oxford Univ. Press, 1999).
O’Donoghue, T. & Rabin, M. Doing it now or later. Am. Econ. Rev. 89, 103–124 (1999).
Kahneman, D. & Klein, G. Conditions for intuitive expertise: a failure to disagree. Am. Psychol. 64, 515–526 (2009).
Battaglia, P. W., Hamrick, J. B. & Tenenbaum, J. B. Simulation as an engine of physical scene understanding. Proc. Natl Acad. Sci. USA 110, 18327–18332 (2013).
Jara-Ettinger, J., Gweon, H., Schulz, L. E. & Tenenbaum, J. B. The naïve utility calculus: computational principles underlying commonsense psychology. Trends Cogn. Sci. 20, 589–604 (2016).
Lohse, G. L. & Johnson, E. J. A comparison of two process tracing methods for choice tasks. Organ. Behav. Hum. Decis. Process. 68, 28–43 (1996).
Hunt, L. T. et al. Formalizing planning and information search in naturalistic decision-making. Nat. Neurosci. 24, 1051–1064 (2021).
Ongchoco, J. D., Jara-Ettinger, J. & Knobe, J. Imagining the good: an offline tendency to simulate good options even when no decision has to be made. In Proc. Annual Meeting of the Cognitive Science Society (eds Goel, A. K. et al.) 904–910 (Cognitive Science Society, 2019).
Ho, M. K., Abel, D., Cohen, J., Littman, M. & Griffiths, T. The efficiency of human cognition reflects planned information processing. In Proc. AAAI Conference on Artificial Intelligence Vol. 34, 1300–1307 (AAAI Press, 2020).
Solway, A. et al. Optimal behavioral hierarchy. PLoS Comput. Biol. 10, e1003779 (2014).
Lieder, F. & Griffiths, T. L. Strategy selection as rational metareasoning. Psychol. Rev. 124, 762–794 (2017).
Krueger, P. M., Lieder, F. & Griffiths, T. L. Enhancing metacognitive reinforcement learning using reward structures and feedback. In Proc. Annual Meeting of the Cognitive Science Society (eds Gunzelmann, G. et al.) 2469–2474 (Cognitive Science Society, 2017).
Rahnev, D. & Denison, R. N. Suboptimality in perceptual decision making. Behav. Brain Sci. 41, e223 (2018).
Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effects models using lme4. J. Stat. Softw. 67, 1–48 (2015).
Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).
Acknowledgements
This work was supported by grant number ONR MURI N00014-13-1-0341, grant number AFOSR 9550-18-1-0077, a grant from the Templeton World Charity Foundation and a grant from Facebook Reality Labs. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
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F.C., F.L., B.v.O. and T.L.G. designed the studies. F.C., F.L. and T.L.G. devised the main model. F.C., S.G., P.D. and B.v.O. devised the alternative models. F.C. implemented the model, collected the data, performed the analyses and drafted the manuscript. T.L.G. and F.L. supervised all aspects of the project. All authors discussed the results and revised the manuscript.
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Callaway, F., van Opheusden, B., Gul, S. et al. Rational use of cognitive resources in human planning. Nat Hum Behav 6, 1112–1125 (2022). https://doi.org/10.1038/s41562-022-01332-8
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DOI: https://doi.org/10.1038/s41562-022-01332-8