Rahnev & Denison's (R&D) extensive review of the perceptual decision-making literature points to the fact that human behavior substantially deviates from optimality. Notably, R&D define optimality according to a standard Bayesian framework (henceforth, the “benchmark model”). Here, we would like to support and elaborate on the claim that this benchmark model has limited validity in describing perceptual decisions. However, rather than addressing the descriptive (in)ability of the model to account for behavioral data, we would like to go a step further and postulate that this model has limited normative validity once constraints of information processing in biological brains are taken into account.
Specifically, we argue that the assumptions of the benchmark model are over-simplistic, considering how perceptual processing is implemented in biological brains, and that under more realistic assumptions the benchmark model ceases to be optimal. A key assumption in the benchmark model is that encoding noise is the sole corrupting element of perceptual decisions (sect. 2.2). Alas, decision-making operations are never limited to stimulus encoding. Rather, they involve a sequential cascade of processes past the encoding stage, such as integration of information across different sources, mental inference, decision formation, response selection, and motor execution. In biological brains, these processes are performed across a hierarchy of cortical layers, which are prone to different sources of noise (Servan-Schreiber et al. Reference Servan-Schreiber, Printz and Cohen1990). Hence, perceptual choices are unavoidably corrupted by “late,” post-encoding, noise. This notion was corroborated in a recent study that dissociated the contributions of three noise sources to decision suboptimality: sensory encoding, response selection, and mental inference (Drugowitsch et al. Reference Drugowitsch, Wyart, Devauchelle and Koechlin2016). Strikingly, noise in mental inference, rather than encoding, was found to be the main contributor to suboptimality.
Here, we argue that in the presence of post-encoding sources of noise, the benchmark model ceases to be optimal. As we next show, higher accuracy can be obtained by down-weighting some aspects of the available information via a “selective integration” process (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a; Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016b; see Osmmy et al. [Reference Osmmy, Moran, Pfeffer, Tsetsos, Usher and Donner2013] for an illustration of how a different form of information down-weighting can facilitate signal detection performance).
To illustrate the superiority of the selective integration model, we consider a simple binary choice scenario, as in R&D's Figure 1. We assumed that the measurement distributions of these two stimuli are N( ± 1, 0.72), that both stimuli are presented with equal prior probabilities, and that observers are awarded or penalized one point for each right or erroneous choice, respectively. Critically, unlike R&D, we assumed that predicted action costs calculated by observers are prone to an additional source of late Gaussian noise denoted by N(0, ξ 2). Note that this late noise affects only the costs that observers predict but not the actual rewards and penalties they receive (± 1). We assumed that late noise is independent across actions and independent of the encoding noise. Using R&D's notations, the predicted cost of each action is as follows:
According to the benchmark model, the chosen action on each trial minimizes predicted cost:
Unsurprisingly, the actually realized cost of the model-selected action increases as a function of late noise, ξ (Fig. 1). Focal to our interest, however, is the comparison between the benchmark and the selective integration models. In the selective integration model, cost predictions are based on “pseudo-likelihoods” l ′ defined as follows:
where w <1 (in Fig. 1, w = 0.1). Note that the pseudo-likelihood equals the standard likelihood for the more likely of the two stimuli. However, the likelihood of the less likely stimulus is selectively down-weighted. Action selection is determined by minimization of the predicted pseudo-costs:
By down-weighting the likelihood of the less likely stimulus, observers attenuate the harmful influences that late noise exerts on performance (see Tsetsos et al. [Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a] for a detailed discussion). Indeed, the selective integration model strikingly outperforms the benchmark model by achieving lower actual costs (Fig. 1; negative costs correspond to positive gains). Therefore, the benchmark model is suboptimal when post-encoding noise is present and is thus an inadequate standard for assessing optimality in behavior. We recently showed that an intriguing violation of rational choice theory, intransitivity of choices, was a by-product of adaptive selective integration processes (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a). Future research should investigate whether and which of the sundry “suboptimal” behaviors reviewed by R&D actually reflect biologically constrained adaptive processes.
Next, we wish to qualify R&D's arguments about the overall utility of assessing optimality (sect. 4). Although we agree that addressing optimality should not be in itself the ultimate goal of the study of perception, we still think that the notion of optimality can serve as an important driver to scientific progress. From an evolutionary perspective, perceptual processing reflects an extended adaptation process and, as such, is ex ante expected to be optimal (Moran Reference Moran2015). Therefore, when theories of optimality are defined appropriately, taking into account the biological constraints of human information processing, they can provide an invaluable benchmark, guiding both theory development and behavioral assessments. On the one hand, when organisms are found to behave optimally, it raises questions about how optimality is achieved at the algorithmic and implementation levels. When, on the other hand, suboptimal behaviors are found, it raises questions pertaining to why these alleged deviations from optimality occur. Such questions can lead to a better understating of the constraints and limitations of human information processing (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a), of the cost function that neural systems strive to minimize (Soltani et al. Reference Soltani, De Martino and Camerer2012), and of the statistical structure of the environment in which cognitive processes evolved (Fawcett et al. Reference Fawcett, Fallenstein, Higginson, Houston, Mallpress, Trimmer and McNamara2014). This understating often leads to a subtler definition of optimality, which supports novel behavioral hypotheses and assessments. In sum, we conceive of scientific progress as an iterative process, in which the notion of optimality, rather than being relinquished, continually evolves and undergoes refinement. It is challenging to define optimality, but we nevertheless think that such attempts are instrumental in scientific progress.
Rahnev & Denison's (R&D) extensive review of the perceptual decision-making literature points to the fact that human behavior substantially deviates from optimality. Notably, R&D define optimality according to a standard Bayesian framework (henceforth, the “benchmark model”). Here, we would like to support and elaborate on the claim that this benchmark model has limited validity in describing perceptual decisions. However, rather than addressing the descriptive (in)ability of the model to account for behavioral data, we would like to go a step further and postulate that this model has limited normative validity once constraints of information processing in biological brains are taken into account.
Specifically, we argue that the assumptions of the benchmark model are over-simplistic, considering how perceptual processing is implemented in biological brains, and that under more realistic assumptions the benchmark model ceases to be optimal. A key assumption in the benchmark model is that encoding noise is the sole corrupting element of perceptual decisions (sect. 2.2). Alas, decision-making operations are never limited to stimulus encoding. Rather, they involve a sequential cascade of processes past the encoding stage, such as integration of information across different sources, mental inference, decision formation, response selection, and motor execution. In biological brains, these processes are performed across a hierarchy of cortical layers, which are prone to different sources of noise (Servan-Schreiber et al. Reference Servan-Schreiber, Printz and Cohen1990). Hence, perceptual choices are unavoidably corrupted by “late,” post-encoding, noise. This notion was corroborated in a recent study that dissociated the contributions of three noise sources to decision suboptimality: sensory encoding, response selection, and mental inference (Drugowitsch et al. Reference Drugowitsch, Wyart, Devauchelle and Koechlin2016). Strikingly, noise in mental inference, rather than encoding, was found to be the main contributor to suboptimality.
Here, we argue that in the presence of post-encoding sources of noise, the benchmark model ceases to be optimal. As we next show, higher accuracy can be obtained by down-weighting some aspects of the available information via a “selective integration” process (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a; Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016b; see Osmmy et al. [Reference Osmmy, Moran, Pfeffer, Tsetsos, Usher and Donner2013] for an illustration of how a different form of information down-weighting can facilitate signal detection performance).
To illustrate the superiority of the selective integration model, we consider a simple binary choice scenario, as in R&D's Figure 1. We assumed that the measurement distributions of these two stimuli are N( ± 1, 0.72), that both stimuli are presented with equal prior probabilities, and that observers are awarded or penalized one point for each right or erroneous choice, respectively. Critically, unlike R&D, we assumed that predicted action costs calculated by observers are prone to an additional source of late Gaussian noise denoted by N(0, ξ 2). Note that this late noise affects only the costs that observers predict but not the actual rewards and penalties they receive (± 1). We assumed that late noise is independent across actions and independent of the encoding noise. Using R&D's notations, the predicted cost of each action is as follows:
Comparison between the Bayesian “benchmark” and the selective integration models. Average actual cost is displayed as a function of late noise (ξ). For simulation code, see https://osf.io/gexrd/?view_only=aa02df150be94beebf310f1e56cec16f.
According to the benchmark model, the chosen action on each trial minimizes predicted cost:
Unsurprisingly, the actually realized cost of the model-selected action increases as a function of late noise, ξ (Fig. 1). Focal to our interest, however, is the comparison between the benchmark and the selective integration models. In the selective integration model, cost predictions are based on “pseudo-likelihoods” l ′ defined as follows:
where w <1 (in Fig. 1, w = 0.1). Note that the pseudo-likelihood equals the standard likelihood for the more likely of the two stimuli. However, the likelihood of the less likely stimulus is selectively down-weighted. Action selection is determined by minimization of the predicted pseudo-costs:
By down-weighting the likelihood of the less likely stimulus, observers attenuate the harmful influences that late noise exerts on performance (see Tsetsos et al. [Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a] for a detailed discussion). Indeed, the selective integration model strikingly outperforms the benchmark model by achieving lower actual costs (Fig. 1; negative costs correspond to positive gains). Therefore, the benchmark model is suboptimal when post-encoding noise is present and is thus an inadequate standard for assessing optimality in behavior. We recently showed that an intriguing violation of rational choice theory, intransitivity of choices, was a by-product of adaptive selective integration processes (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a). Future research should investigate whether and which of the sundry “suboptimal” behaviors reviewed by R&D actually reflect biologically constrained adaptive processes.
Next, we wish to qualify R&D's arguments about the overall utility of assessing optimality (sect. 4). Although we agree that addressing optimality should not be in itself the ultimate goal of the study of perception, we still think that the notion of optimality can serve as an important driver to scientific progress. From an evolutionary perspective, perceptual processing reflects an extended adaptation process and, as such, is ex ante expected to be optimal (Moran Reference Moran2015). Therefore, when theories of optimality are defined appropriately, taking into account the biological constraints of human information processing, they can provide an invaluable benchmark, guiding both theory development and behavioral assessments. On the one hand, when organisms are found to behave optimally, it raises questions about how optimality is achieved at the algorithmic and implementation levels. When, on the other hand, suboptimal behaviors are found, it raises questions pertaining to why these alleged deviations from optimality occur. Such questions can lead to a better understating of the constraints and limitations of human information processing (Tsetsos et al. Reference Tsetsos, Moran, Moreland, Chater, Usher and Summerfield2016a), of the cost function that neural systems strive to minimize (Soltani et al. Reference Soltani, De Martino and Camerer2012), and of the statistical structure of the environment in which cognitive processes evolved (Fawcett et al. Reference Fawcett, Fallenstein, Higginson, Houston, Mallpress, Trimmer and McNamara2014). This understating often leads to a subtler definition of optimality, which supports novel behavioral hypotheses and assessments. In sum, we conceive of scientific progress as an iterative process, in which the notion of optimality, rather than being relinquished, continually evolves and undergoes refinement. It is challenging to define optimality, but we nevertheless think that such attempts are instrumental in scientific progress.