Degenerate Boundaries for Multiple-alternative Decisions

Overview

Journal Nat Commun

Specialty Biology

Date 2022 Aug 29

PMID 36038538

Authors

Sophie-Anne Baker

Thom Griffith

Nathan F Lepora

Affiliations

Soon will be listed here.

Abstract

Integration-to-threshold models of two-choice perceptual decision making have guided our understanding of human and animal behavior and neural processing. Although such models seem to extend naturally to multiple-choice decision making, consensus on a normative framework has yet to emerge, and hence the implications of threshold characteristics for multiple choices have only been partially explored. Here we consider sequential Bayesian inference and a conceptualisation of decision making as a particle diffusing in n-dimensions. We show by simulation that, within a parameterised subset of time-independent boundaries, the optimal decision boundaries comprise a degenerate family of nonlinear structures that jointly depend on the state of multiple accumulators and speed-accuracy trade-offs. This degeneracy is contrary to current 2-choice results where there is a single optimal threshold. Such boundaries support both stationary and collapsing thresholds as optimal strategies for decision-making, both of which result from stationary representations of nonlinear boundaries. Our findings point towards a normative theory of multiple-choice decision making, provide a characterisation of optimal decision thresholds under this framework, and inform the debate between stationary and dynamic decision boundaries for optimal decision making.

References

Bogacz R, Usher M, Zhang J, McClelland J . Extending a biologically inspired model of choice: multi-alternatives, nonlinearity and value-based multidimensional choice. Philos Trans R Soc Lond B Biol Sci. 2007; 362(1485):1655-70. PMC: 2440778. DOI: 10.1098/rstb.2007.2059. View

Malhotra G, Leslie D, Ludwig C, Bogacz R . Time-varying decision boundaries: insights from optimality analysis. Psychon Bull Rev. 2017; 25(3):971-996. PMC: 5990589. DOI: 10.3758/s13423-017-1340-6. View

Bogacz R, Hu P, Holmes P, Cohen J . Do humans produce the speed-accuracy trade-off that maximizes reward rate?. Q J Exp Psychol (Hove). 2009; 63(5):863-91. PMC: 2908414. DOI: 10.1080/17470210903091643. View

Hanks T, Ditterich J, Shadlen M . Microstimulation of macaque area LIP affects decision-making in a motion discrimination task. Nat Neurosci. 2006; 9(5):682-9. PMC: 2770004. DOI: 10.1038/nn1683. View

Bogacz R, Brown E, Moehlis J, Holmes P, Cohen J . The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychol Rev. 2006; 113(4):700-65. DOI: 10.1037/0033-295X.113.4.700. View

Churchland A, Ditterich J . New advances in understanding decisions among multiple alternatives. Curr Opin Neurobiol. 2012; 22(6):920-6. PMC: 3422607. DOI: 10.1016/j.conb.2012.04.009. View

Standage D, Blohm G, Dorris M . On the neural implementation of the speed-accuracy trade-off. Front Neurosci. 2014; 8:236. PMC: 4131279. DOI: 10.3389/fnins.2014.00236. View

Gluth S, Spektor M, Rieskamp J . Value-based attentional capture affects multi-alternative decision making. Elife. 2018; 7. PMC: 6218187. DOI: 10.7554/eLife.39659. View

Gold J, Shadlen M . The neural basis of decision making. Annu Rev Neurosci. 2007; 30:535-74. DOI: 10.1146/annurev.neuro.29.051605.113038. View

10.

Usher M, McClelland J . The time course of perceptual choice: the leaky, competing accumulator model. Psychol Rev. 2001; 108(3):550-92. DOI: 10.1037/0033-295x.108.3.550. View

11.

Bogacz R, Gurney K . The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Comput. 2007; 19(2):442-77. DOI: 10.1162/neco.2007.19.2.442. View

12.

Simen P, Contreras D, Buck C, Hu P, Holmes P, Cohen J . Reward rate optimization in two-alternative decision making: empirical tests of theoretical predictions. J Exp Psychol Hum Percept Perform. 2009; 35(6):1865-97. PMC: 2791916. DOI: 10.1037/a0016926. View

13.

Voskuilen C, Ratcliff R, Smith P . Comparing fixed and collapsing boundary versions of the diffusion model. J Math Psychol. 2017; 73:59-79. PMC: 5450920. DOI: 10.1016/j.jmp.2016.04.008. View

14.

Van Maanen L, Grasman R, Forstmann B, Keuken M, Brown S, Wagenmakers E . Similarity and number of alternatives in the random-dot motion paradigm. Atten Percept Psychophys. 2012; 74(4):739-53. PMC: 3310993. DOI: 10.3758/s13414-011-0267-7. View

15.

Drugowitsch J, Moreno-Bote R, Churchland A, Shadlen M, Pouget A . The cost of accumulating evidence in perceptual decision making. J Neurosci. 2012; 32(11):3612-28. PMC: 3329788. DOI: 10.1523/JNEUROSCI.4010-11.2012. View

16.

Bogacz R, Wagenmakers E, Forstmann B, Nieuwenhuis S . The neural basis of the speed-accuracy tradeoff. Trends Neurosci. 2009; 33(1):10-6. DOI: 10.1016/j.tins.2009.09.002. View

17.

Roitman J, Shadlen M . Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J Neurosci. 2002; 22(21):9475-89. PMC: 6758024. View

18.

Friston K, Kilner J, Harrison L . A free energy principle for the brain. J Physiol Paris. 2006; 100(1-3):70-87. DOI: 10.1016/j.jphysparis.2006.10.001. View

19.

Louie K, Khaw M, Glimcher P . Normalization is a general neural mechanism for context-dependent decision making. Proc Natl Acad Sci U S A. 2013; 110(15):6139-44. PMC: 3625302. DOI: 10.1073/pnas.1217854110. View

20.

Lepora N, Gurney K . The basal ganglia optimize decision making over general perceptual hypotheses. Neural Comput. 2012; 24(11):2924-45. DOI: 10.1162/NECO_a_00360. View