Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Rational use of cognitive resources in human planning

Subjects

A Publisher Correction to this article was published on 16 June 2022

This article has been updated

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Formalizing planning under computational constraints.
Fig. 2: Experimental task.
Fig. 3: Experiment 1 results.
Fig. 4: Experiment 2 results.
Fig. 5: Experiment 3 results.
Fig. 6: Experiment 4 results.

Similar content being viewed by others

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

References

  1. Huys, Q. J. M. et al. Interplay of approximate planning strategies. Proc. Natl Acad. Sci. USA 112, 3098–3103 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. 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).

  4. 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).

    Article  CAS  PubMed  Google Scholar 

  5. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. 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).

  7. Snider, J., Lee, D., Poizner, H. & Gepshtein, S. Prospective optimization with limited resources. PLoS Comput. Biol. 11, e1004501 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  8. Von Neumann, J. & Morgenstern, O. The Theory of Games and Economic Behavior (Princeton Univ. Press, 1944).

  9. Stahl, D. O. & Wilson, P. W. Experimental evidence on players’ models of other players. J. Econ. Behav. Organ. 25, 309–327 (1994).

    Article  Google Scholar 

  10. Camerer, C. F., Ho, T.-H. & Chong, J.-K. A cognitive hierarchy model of games. Q. J. Econ. 119, 861–898 (2004).

    Article  Google Scholar 

  11. Newell, A. & Simon, H. The logic theory machine—a complex information processing system. IRE Trans. Inform. Theory 2, 61–79 (1956).

    Article  Google Scholar 

  12. 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).

    Article  Google Scholar 

  13. 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).

  14. Newell, A. et al. Human Problem Solving Vol. 104 (Prentice-Hall, 1972).

  15. Kool, W., Gershman, S. J. & Cushman, F. A. Cost–benefit arbitration between multiple reinforcement-learning systems. Psychol. Sci. 28, 1321–1333 (2017).

    Article  PubMed  Google Scholar 

  16. Norris, D. & Cutler, A. More why, less how: what we need from models of cognition. Cognition 213, 104688 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  17. Marr, D. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (WH Freeman, 1982).

  18. Anderson, J. R. The Adaptive Character of Thought (Psychology Press, 1990).

  19. Savage, L. J. The Foundations of Statistics (John Wiley & Sons, 1954).

  20. Tenenbaum, J. B. & Griffiths, T. L. Generalization, similarity and Bayesian inference. Behav. Brain Sci. 24, 629–640 (2001).

    Article  CAS  PubMed  Google Scholar 

  21. Anderson, J. R. The adaptive nature of human categorization. Psychol. Rev. 98, 409–429 (1991).

    Article  Google Scholar 

  22. Ashby, F. G. & Alfonso-Reese, L. A. Categorization as probability density estimation. J. Math. Psychol. 39, 216–233 (1995).

    Article  Google Scholar 

  23. Knill, D. C. & Richards, W. Perception as Bayesian Inference (Cambridge Univ. Press, 1996).

  24. Oaksford, M. & Chater, N. A rational analysis of the selection task as optimal data selection. Psychol. Rev. 101, 608–631 (1994).

    Article  Google Scholar 

  25. Gureckis, T. M. & Markant, D. B. Self-directed learning: a cognitive and computational perspective. Perspect. Psychol. Sci. 7, 464–481 (2012).

    Article  PubMed  Google Scholar 

  26. 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).

    Article  PubMed  Google Scholar 

  27. Lewis, R. L., Howes, A. & Singh, S. Computational rationality: linking mechanism and behavior through bounded utility maximization. Top. Cogn. Sci. 6, 279–311 (2014).

    Article  PubMed  Google Scholar 

  28. 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).

    Article  CAS  PubMed  Google Scholar 

  29. 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).

    Article  PubMed  Google Scholar 

  30. 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).

  31. Simon, H. A. A behavioral model of rational choice. Q. J. Econ. 69, 99–118 (1955).

    Article  Google Scholar 

  32. 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).

    Article  PubMed  Google Scholar 

  33. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Tajima, S., Drugowitsch, J. & Pouget, A. Optimal policy for value-based decision-making. Nat. Commun. 7, 12400 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Tajima, S., Drugowitsch, J., Patel, N. & Pouget, A. Optimal policy for multi-alternative decisions. Nat. Neurosci. 22, 1503–1511 (2019).

    Article  CAS  PubMed  Google Scholar 

  36. Fudenberg, D., Strack, P. & Strzalecki, T. Speed, accuracy, and the optimal timing of choices. Am. Econ. Rev. 108, 3651–3684 (2018).

    Article  Google Scholar 

  37. Callaway, F., Rangel, A. & Griffiths, T. L. Fixation patterns in simple choice reflect optimal information sampling. PLoS Comput. Biol. 17, e1008863 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Jang, A. I., Sharma, R. & Drugowitsch, J. Optimal policy for attention-modulated decisions explains human fixation behavior. eLife 10, e63436 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. 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).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  40. Mattar, M. G. & Daw, N. D. Prioritized memory access explains planning and hippocampal replay. Nat. Neurosci. 21, 1609–1617 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Matheson, J. E. The economic value of analysis and computation. IEEE Trans. Syst. Sci. Cybern. 4, 325–332 (1968).

    Article  Google Scholar 

  42. 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).

  43. Russell, S. & Wefald, E. Principles of metareasoning. Artif. Intell. 49, 361–395 (1991).

    Article  Google Scholar 

  44. 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).

    Article  Google Scholar 

  45. 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).

    Article  CAS  PubMed  Google Scholar 

  46. Keramati, M., Dezfouli, A. & Piray, P. Speed/accuracy trade-off between the habitual and the goal-directed processes. PLoS Comput. Biol. 7, e1002055 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Shenhav, A., Botvinick, M. & Cohen, J. The expected value of control: an integrative theory of anterior cingulate cortex function. Neuron 79, 217–240 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Kool, W. & Botvinick, M. Mental labour. Nat. Hum. Behav. 2, 899–908 (2018).

    Article  PubMed  Google Scholar 

  49. 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).

  50. Russell, S. J. & Norvig, P. Artificial Intelligence: A Modern Approach (Prentice Hall, 2002).

  51. Solway, A. & Botvinick, M. M. Evidence integration in model-based tree search. Proc. Natl Acad. Sci. USA 112, 11708–11713 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. De Groot, A. D. Thought and Choice in Chess (Grouton, 1965).

  53. Chase, W. G. & Simon, H. A. Perception in chess. Cogn. Psychol. 4, 55–81 (1973).

    Article  Google Scholar 

  54. 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).

    Article  Google Scholar 

  55. 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).

    Article  Google Scholar 

  56. Payne, J. W., Bettman, J. R. & Johnson, E. J. The Adaptive Decision Maker (Cambridge Univ. Press, 1993).

  57. 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).

    Article  Google Scholar 

  58. 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).

  59. Ratcliff, R. & Smith, P. L. A comparison of sequential sampling models for two-choice reaction time. Psychol. Rev. 111, 333–367 (2004).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Teodorescu, A. R. & Usher, M. Disentangling decision models: from independence to competition. Psychol. Rev. 120, 1–38 (2013).

    Article  PubMed  Google Scholar 

  61. McMillen, T. & Holmes, P. The dynamics of choice among multiple alternatives. J. Math. Psychol. 50, 30–57 (2006).

    Article  Google Scholar 

  62. Piantadosi, S. T. One parameter is always enough. AIP Adv. 8, 095118 (2018).

    Article  Google Scholar 

  63. 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).

  64. Gigerenzer, G. Why heuristics work. Perspect. Psychol. Sci. 3, 20–29 (2008).

    Article  PubMed  Google Scholar 

  65. Gigerenzer, G. & Gaissmaier, W. Heuristic decision making. Annu. Rev. Psychol. 62, 451–482 (2011).

    Article  PubMed  Google Scholar 

  66. Todd, P. M. & Gigerenzer, G. Bounding rationality to the world. J. Econ. Psychol. 24, 143–165 (2003).

    Article  Google Scholar 

  67. Gigerenzer, G. & Goldstein, D. G. Reasoning the fast and frugal way: models of bounded rationality. Psychol. Rev. 103, 650–659 (1996).

    Article  CAS  PubMed  Google Scholar 

  68. Gigerenzer, G. & Todd, P. M. Simple Heuristics That Make Us Smart (Oxford Univ. Press, 1999).

  69. O’Donoghue, T. & Rabin, M. Doing it now or later. Am. Econ. Rev. 89, 103–124 (1999).

    Article  Google Scholar 

  70. Kahneman, D. & Klein, G. Conditions for intuitive expertise: a failure to disagree. Am. Psychol. 64, 515–526 (2009).

    Article  PubMed  Google Scholar 

  71. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. 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).

    Article  PubMed  Google Scholar 

  73. 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).

    Article  Google Scholar 

  74. Hunt, L. T. et al. Formalizing planning and information search in naturalistic decision-making. Nat. Neurosci. 24, 1051–1064 (2021).

    Article  CAS  PubMed  Google Scholar 

  75. 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).

  76. 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).

  77. Solway, A. et al. Optimal behavioral hierarchy. PLoS Comput. Biol. 10, e1003779 (2014).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  78. Lieder, F. & Griffiths, T. L. Strategy selection as rational metareasoning. Psychol. Rev. 124, 762–794 (2017).

    Article  PubMed  Google Scholar 

  79. 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).

  80. Rahnev, D. & Denison, R. N. Suboptimality in perceptual decision making. Behav. Brain Sci. 41, e223 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  81. Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effects models using lme4. J. Stat. Softw. 67, 1–48 (2015).

    Article  Google Scholar 

  82. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Frederick Callaway.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Peer Review File Nature Human Behaviour thanks Mike Oaksford and Maarten Speekenbrink for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Methods, Results, Tables 1 and 2, and Figs. 1 and 2.

Reporting Summary

Peer Review File

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41562-022-01332-8

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing