We agree with Lieder and Griffiths (L&G) that when combined with reasonable assumptions about human cognitive capacities and limitations, the principle of bounded optimality provides a realistic normative standard for cognitive operations and representations. Indeed, L&G apply this standard to effectively argue that a wide range of human cognitive behaviors can be viewed as resulting from an optimal use of limited resources. We were surprised however, that they did not extend their analysis to consider human behavior during cognitive development. Specifically, we feel that cognition during early development provides particularly powerful insight into the debate between bounded optimality and true sub-optimality, precisely because young children have limited computational and cognitive resources. Moreover, there are relatively straightforward ways of estimating these resource limitations, and how they might be changing across development, rather than having to make assumptions about how limiting they might be.

Extensive research with human adults has documented that they are adept at mitigating the influence of sensory uncertainty on task performance by integrating sensory cues with learned prior information, in a Bayes-optimal fashion (Bejjanki et al. Reference Bejjanki, Knill and Aslin2016; Berniker et al. Reference Berniker, Voss and Kording2010; Jazayeri & Shadlen Reference Jazayeri and Shadlen2010; Körding & Wolpert Reference Körding and Wolpert2004; Kwon & Knill Reference Kwon and Knill2013; Stocker & Simoncelli Reference Stocker and Simoncelli2006; Tassinari et al. Reference Tassinari, Hudson and Landy2006). Further research has shown that young children and infants are sensitive to environmental regularities, and that the ability to learn and use such regularities is involved in the development of several cognitive abilities (Fiser & Aslin Reference Fiser and Aslin2002; Gopnik et al. Reference Gopnik, Sobel, Schulz and Glymour2001; Jusczyk & Aslin Reference Jusczyk and Aslin1995; Kirkham et al. Reference Kirkham, Slemmer and Johnson2002; Kuhl & Meltzoff Reference Kuhl and Meltzoff1982; Neil et al. Reference Neil, Chee-Ruiter, Scheier, Lewkowicz and Shimojo2006; Saffran et al. Reference Saffran, Aslin and Newport1996; Xu & Garcia Reference Xu and Garcia2008). However, it has also been reported that children younger than 8–12 years of age demonstrate substantial deficits in their ability to optimally mitigate the influence of sensory uncertainty by using multiple sources of information (Barutchu et al. Reference Barutchu, Crewther and Crewther2008; Chambers et al. Reference Chambers, Sokhey, Gaebler-Spira and Kording2018; Gori et al. Reference Gori, Del Viva, Sandini and Burr2008; Nardini et al. Reference Nardini, Bedford and Mareschal2010; Nardini et al. Reference Nardini, Jones, Bedford and Braddick2008; Petrini et al. Reference Petrini, Remark, Smith and Nardini2014). Some have suggested that the basis for this sub-optimality is a deficiency in the fundamental computational mechanism involved in combining two or more sources of information, which might take 8–12 years to fully mature. Applying the resource-rational analysis to this problem suggests an alternative possibility (as highlighted by L&G): “[children's] heuristics might already make optimal use of their cognitive resources but the computational complexity of the problem might exceed their cognitive capacities.” Indeed, we have recently found (Bejjanki et al. Reference Bejjanki, Randrup and Aslin2019) that 6–7-year-olds are capable of integrating learned regularities with sensory information in a statistically optimal manner (that is indistinguishable from adults), provided that task complexity is reduced. Performance in tasks involving greater complexity necessitates the deployment of sophisticated top-down mechanisms (e.g., cognitive control, executive function, etc.) that typically do not reach adult-like levels until early adolescence (Best & Miller Reference Best and Miller2010; Carlson et al. Reference Carlson, Zelazo, Faja and Zelazo2013; Davidson et al. Reference Davidson, Amso, Anderson and Diamond2006; Luciana & Nelson Reference Luciana and Nelson1998; Zelazo et al. Reference Zelazo, Anderson, Richler, Wallner-Allen, Beaumont and Weintraub2013). Indeed, several studies have shown that young children's behavior in tasks drawing upon these mechanisms is critically moderated by task complexity. For instance, Luciana and Nelson (Reference Luciana and Nelson1998) found that while 5–7-year-olds were indistinguishable from adults when carrying out simple versions of a spatial working memory task, as task demands increased, performance in 5–7-year-olds, but not adults, deteriorated rapidly. Similarly, Davidson et al. (Reference Davidson, Amso, Anderson and Diamond2006) found that while even 4-year-olds could simultaneously hold information in mind and inhibit a dominant response when rules remained constant, the ability to flexibly switch between rules was not adult-like even in 13-year-olds. Thus, children's inability to demonstrate Bayes-optimal computations in complex tasks might have less to do with their computational capacity and more to do with the immature cognitive resources that are available to them. These findings are therefore consistent with a resource-rational explanation.

More broadly, resource-rational analysis is built on the assumption that cognitive mechanisms are well-adapted to their function, and the cognitive constraints under which they operate. Although L&G briefly allude to a need to understand the process by which cognitive mechanisms are adapted to the constraints at hand via learning or evolution, they do not consider this question, or its implications for cognitive development, in any detail. For instance, their speculation that resource-rational decision mechanisms are provided by evolution or learning during development finesses the key question about how such decision mechanisms are deployed. We argue that the application of resource rational analysis would shed important new light on cognitive development. In particular, considering the bounds imposed by limited cognitive and computational resources should be, but is not currently, an important consideration in developing a normative standard for evaluating cognition across development. As illustrated above, “failures” in young children's ability to carry out sophisticated computations need not be attributed to deficits in the fundamental computational capacity available to children early in development, but rather to ancillary immaturities in general cognitive abilities. Similarly, resource rational analysis can potentially elucidate how and why young children might outperform adults. For instance, young children have an enhanced ability to learn languages. According to one prominent hypothesis (the less is more hypothesis), young children outperform adults in learning languages precisely because their resource constraints limit their ability to entertain complex hypotheses (Hudson Kam & Newport Reference Hudson Kam and Newport2005; Newport Reference Newport1990). Consistent with this hypothesis, Elman (Reference Elman1993) showed that initially resource-constrained neural networks learned grammatical structure better than unconstrained nets – resource constraints prevented the search for complex patterns, keeping networks from getting stuck in local minima. Similarly, Kersten and Earles (Reference Kersten and Earles2001) showed that adults learned miniature artificial languages better when initially presented with only small segments of language than when they were presented immediately with the full complexity of the language. These findings, and indeed the less is more hypothesis, are consistent with the predictions of resource-rational analysis: given limited resources, resource rationality depends on the availability of information that can be optimally exploited by the available cognitive and computational resources.