Resource-rational models maximize some measure of performance while simultaneously minimizing a cognitive or neural resource cost or while simultaneously satisfying a resource constraint. We observe that proposals that all start from this same high-level principle are fairly different in their implications.

To understand this diversity, we believe that it is necessary to pay careful attention to the following model dimensions.

The form of the performance term. The form of the performance term differs widely across models. Some models commit to a specific task and an associated behavioral objective, such as estimation or tracking error (Mackowiak and Wiederholt Reference Mackowiak and Wiederholt2009; Młynarski and Hermundstad Reference Młynarski and Hermundstad2018; Park and Pillow Reference Park and Pillow2017; Sims Reference Sims2003; Sims et al. Reference Sims, Jacobs and Knill2012; van den Berg and Ma Reference van den Berg and Ma2018), categorization accuracy (Li et al. Reference Li, Castañon, Solomon, Vandormael and Summerfield2017; Młynarski and Hermundstad Reference Młynarski and Hermundstad2018; van den Berg and Ma Reference van den Berg and Ma2018), or discriminability (Ganguli and Simoncelli Reference Ganguli and Simoncelli2014). Other models instead use mutual information between stimulus and response as a performance term (Barlow Reference Barlow1961; Laughlin Reference Laughlin1981; Olshausen and Field Reference Olshausen and Field1996; Wei and Stocker Reference Wei and Stocker2015; Zaslavsky et al. Reference Zaslavsky, Kemp, Regier and Tishby2018). The latter approach is meant to be general-purpose rather than task-specific and arguably appropriate for neural codes in early sensory areas, but suboptimal for almost any particular task. Resource-rational modelers need to make an explicit, motivated commitment to a task-specific or a general-purpose performance term, and the field needs to figure out in what situations the brain uses either type. If a model assumes a general-purpose term, its degree of suboptimality in specific tasks should be studied.

The nature of the resource cost or constraint. Similarly, there have been many different formulations of the resource cost/constraint. Some models use an information-theoretic measure of the complexity of internal representations, for example, mutual information as a cost function (Sims Reference Sims2003; Sims et al. Reference Sims, Jacobs and Knill2012), others an algorithmically motivated measure of the intensity of observation or calculation (Shaw and Shaw Reference Shaw and Shaw1977), and yet others an explicitly neural cost (Barlow Reference Barlow1961; Ganguli and Simoncelli Reference Ganguli and Simoncelli2014; Laughlin Reference Laughlin1981; Olshausen and Field Reference Olshausen and Field1996; van den Berg and Ma Reference van den Berg and Ma2018). Another important distinction is between models that assume a cost/constraint on the number of different types of signals that can be sent, regardless of the degree to which the full repertoire is used (Laughlin Reference Laughlin1981; Netzer Reference Netzer2009; Robson Reference Robson2001; Steiner and Stewart Reference Steiner and Stewart2016; Wei and Stocker Reference Wei and Stocker2015; Woodford Reference Woodford2012), and those that assume a cost/constraint on the rate at which signals are actually sent through the system (e.g., whenever the cost/constraint is on mutual information); sometimes constraints of both types are imposed (Ganguli and Simoncelli Reference Ganguli and Simoncelli2014). Finally, some models (such as Laughlin Reference Laughlin1981) assume a hard constraint on the quantity of the resource that can be used, while in others (such as van den Berg and Ma Reference van den Berg and Ma2018) the quantity of the resource is variable but there is an increasing cost of using more of it. The two formulations make different predictions about how the mechanism should be expected to change when the environment changes; the variable-resource version also allows analysis of the question of the optimal allocation of attention or precision across multiple locations or dimensions of a decision problem (Mackowiak and Wiederholt Reference Mackowiak and Wiederholt2009; Shaw and Shaw Reference Shaw and Shaw1977; van den Berg and Ma Reference van den Berg and Ma2018). Beyond the fields discussed in the target article, resource-rational modelers might want to draw inspiration from the theory of optimal feedback control, in which more precise control incurs greater metabolic expenses at the organismal level (Todorov and Jordan Reference Todorov and Jordan2002).

The time scale over which resources are allocated. Attention can be efficiently allocated in response to trial-to-trial variations in reward or priority (Bays Reference Bays2014; Sims Reference Sims2003; van den Berg and Ma Reference van den Berg and Ma2018), in other words, on a timescale of seconds. By contrast, efficient neural codes are often assumed to be optimized with respect to natural statistics (Barlow Reference Barlow1961; Laughlin Reference Laughlin1981), which vary on a much longer timescale. This distinction seems largely aligned with the one made under (1), with shorter timescales being associated with task specificity. Resource-rational models are often non-committal about the timescales over which the optimization occurs. Recent work on efficient codes in nonstationary environments (Młynarski and Hermundstad Reference Młynarski and Hermundstad2018) holds promise for bridging the divide.

Learning to be resource-rational. A question that is not often asked is how resource-rational mechanisms are learned. The target article simply defines a constrained optimum and supposes that “evolution, cognitive development, and life-long learning” have somehow solved it, without saying how. But recognizing that a particular cognitive mechanism is optimal for one's environment requires knowledge of the statistics of the environment, which in practice can never be known with certainty from any finite body of experience. The informational requirements of the learning process may impose constraints on the degree of efficiency of cognitive mechanisms that can be learned, even asymptotically, as discussed, for example, by Robson and Whitehead (Reference Robson and Whitehead2016). The question of how well-adapted a cognitive mechanism can reasonably be assumed to be is even more important if the statistics of the environment are changing (Młynarski and Hermundstad Reference Młynarski and Hermundstad2018).

Are finite-sampling models truly resource-rational models? In some models described in the target article, the observer simulates possible futures – technically, Markov chain Monte Carlo (MCMC) sampling from a posterior (Lieder et al. Reference Lieder, Hsu and Griffiths2014; Reference Lieder2018; Vul et al. Reference Vul, Goodman, Griffiths and Tenenbaum2014). The high-level idea here is that samples represent computational resources, and that those are limited. More samples would correspond to a better approximation of a performance term. However, it is unclear to us if this approach falls into the framework of optimizing a linear combination of a performance term and a resource cost.

Role of reasoning. An ambiguity in references to “resource-rationality” is whether “rationality” is intended to mean the outcome of a process of conscious, logical reasoning, or simply means that something is an efficient solution to a problem, however that solution may have developed (Blume and Easley Reference Blume and Easley1984; Smith Reference Smith2009). Theories of efficient coding in early-stage sensory processing are rather obviously not to be interpreted as hypotheses according to which sensory processing is consciously decided upon; and it seems that in general, the authors of the target article do not have intend “rationality” in this way – the distinction that they draw between the resource-rationality hypothesis and Stigler's (Stigler Reference Stigler1961) model of optimal information gathering indicates this. Nonetheless, this is not clear in all of the references that they cite as examples of the resource-rationality research program. In particular, the more recent economics literature that models the imperfect information of decision makers as reflecting an optimal allocation of limited attention is often written as if the decision as to what to be aware of is made quite deliberately, just as in the work of Stigler.

We view these differences as challenges that need to be addressed but that do not invalidate the overall framework. Progress will require carefully distinguishing between the different formalisms, and finding ways to decide which ones are more applicable to particular settings.