Rahnev & Denison (R&D) have produced a comprehensive survey and incisive critique of optimality hypotheses in perceptual decision research. It is an important and corrective contribution. For us, as for the authors, whether an organism behaves optimally or suboptimally is largely beside the point. What we really want to know is: What are the neural mechanisms underlying perception, cognition and action, and how do they work?

One thing seems clear: Perceptual decision making is fundamentally adaptive. Animal perception is alive with adaption, from performance improvements with practice, to the biasing effects of rewards. But inherent in the concept of adaptation is some form of objective or utility function, such that changes in an organism's behavior tend to increase its value. The authors advocate the development of a standard observer model of perceptual decision making: a model that describes simply what is – not what is ideal. We applaud this proposal, but we venture to guess that a well-defined utility function will be found at the core of any future standard observer model, and that brain mechanisms of adaptation will be most readily uncovered if aided by a well-developed theory of optimality.

The authors advocate ditching the optimal-suboptimal dichotomy altogether, based on their strong position that the optimality concept itself is essentially meaningless. They also cite widespread findings of suboptimal behavior, and they note the problematic coexistence of multiple meanings of optimality in the literature. We agree that terminology abuse is truly a problem. We disagree, however, when the authors cite our own work as evidence of suboptimality in speed-accuracy tradeoff adjustment, even according to an explicitly stated definition – namely, that behavior is optimal if it maximizes the rate of rewards earned for performance (Bogacz et al. Reference Bogacz, Brown, Moehlis, Holmes and Cohen2006).

Our interpretation of our work on speed-accuracy tradeoff adjustment and the reward-rate-optimality hypothesis is that there is strong evidence for reward-rate-optimal tradeoffs in some circumstances. Further, we argue that, far from being a useless concept, optimality analyses have generated interesting and falsifiable predictions about two-choice perceptual decisions. We tested them and found that people, as a group, appeared to be distributed in their behavior around the reward-rate-maximizing speed-accuracy tradeoff (Simen et al. Reference Simen, Contreras, Buck, Hu, Holmes and Cohen2009). We also found that individually, people exhibited striking transitions between fast guessing and evidence accumulation in a manner consistent with some of the most intuition-defying predictions, in Bogacz et al. (Reference Bogacz, Brown, Moehlis, Holmes and Cohen2006), of a diffusion model with reward-rate-optimal boundary and starting point parameters

Most importantly, we found that there are some decision-task features that people can handle almost reward rate optimally with sufficient training, whereas there are others for which they remain notably suboptimal. In short, people tend to shift toward the reward-rate-optimal speed-accuracy tradeoff when changes in a task have to do with time or rate. For example, the reward-rate-optimal speed-accuracy tradeoff favors speed for shorter inter-trial delays but accuracy for longer delays. There is good evidence that people not only adapt in the direction predicted by reward-rate-optimality, but that they (at least young participants) come very close to achieving optimality when the incentive structure is clear (Evans & Brown Reference Evans and Brown2017; Simen et al. Reference Simen, Contreras, Buck, Hu, Holmes and Cohen2009; Starns & Ratcliff Reference Starns and Ratcliff2010). Our participants collectively appeared to be clustered in their boundary and starting point parameter settings around the ideal observer values, earning 97%–99% of the maximum possible reward. Participants did exhibit a slight, but consistent over-emphasis on accuracy. This is evidence for suboptimality, but only in the sense that 3.14 does not equal pi.

On the other hand, our participants tended to fail miserably to approximate optimal performance when it was the signal-to-noise ratio that changed across conditions (Balcı et al. Reference Balcı, Simen, Niyogi, Saxe, Hughes, Holmes and Cohen2011b). That failure may have an explanation in terms of the reward-rate-optimality hypothesis. Contrary to what is stated in the first paragraph of section 3.4, the reward-rate-optimal tradeoff is non-monotonic over the range of possible signal-to-noise ratios. For very high and low signal-to-noise ratios, one should decide quickly; only when the signal-to-noise ratio is at an intermediate level should one slow down to boost accuracy (Bogacz et al. Reference Bogacz, Brown, Moehlis, Holmes and Cohen2006). Only an optimality analysis reveals this prediction, and tests of it reveal that most people do not follow it when the signal-to-noise ratio is low, though our highest-earning participants did. At very low signal-to-noise ratios, it is difficult to tell whether one should try harder or give up and guess. Further, although decreasing decision thresholds within trials are required by reward-rate-optimality in many circumstances, we found that fixed thresholds within trials gave the most parsimonious account of our data (Karşılar et al. Reference Karşılar, Simen, Papadakis and Balcı2014).

We conclude from these findings that when simple heuristics allow near-optimal computation, people can and often do implement those heuristics and adapt toward optimality. Time is a dimension in which people and animals routinely show evidence of reward-rate-optimal performance. Signal-to-noise ratio just is not. In fact, when it comes to timing tasks, people and animals show striking conformance with predictions of the reward-rate-optimality hypothesis (e.g., Balcı et al. Reference Balcı, Freestone and Gallistel2009; Reference Balcı, Freestone, Simen, deSouza, Cohen and Holmes2011a; Çavdaroğlu et al. Reference Çavdaroglu, Zeki and Balcı2014; Simen et al. Reference Simen, Balcı, deSouza, Holmes and Cohen2011).

We agree with the authors that the term “optimal” is widely used with different meanings. Bayesian modelers frequently describe models that incorporate new evidence according to Bayes’ rule to be “optimal.” Implicit in this assumption is that accurate evidence updating will automatically yield whatever sort of optimal outcome you ultimately choose to define. Yet added to the general computational intractability of Bayesian inference, the best rules for reading out that evidence into choices may themselves be intractable (e.g., with more than two options; McMillen & Holmes Reference McMillen and Holmes2006). Surely then, heuristics are the best we can do, in general.

Nonetheless, optimality hypotheses can aid the development of suboptimal, heuristic models that adhere to plausible constraints. For example, reward-rate-optimality motivated our development of a heuristic neural network model that nearly optimizes speed-accuracy tradeoffs when tasks speed up or slow down, but that fails to adapt to changes in signal-to-noise ratio (Simen et al. Reference Simen, Cohen and Holmes2006) – a behavioral pattern we later observed. Optimality analyses may therefore advance the standard observer model goal by establishing usable benchmarks for heuristic designers to exploit during the model-design phase. Hence, the scientific reward-rate-optimal theoretical stance may involve more optimality theory than the authors recommend.