Use of an optimality approach has been remarkably successful in many different domains of the natural sciences. Its application to biological organisms equipped with a well-developed central nervous system (CNS) is generally based on the fact that these organisms learn, thus optimizing their behavior. Hence, a well-learned behavior can be considered optimized, and various features of such behavior can be explained as a result of optimization with respect to a specific criterion (also known as cost function). The explanatory power is perhaps the main advantage of an optimality approach. To fully benefit from that advantage, an optimality approach should be applied to the entire behavioral paradigm. However, the suggestion of Rahnev & Denison (R&D) to abandon the optimality approach is based on examples of suboptimality obtained through application of an optimality approach to the decision rule only. Here we argue that this suboptimality is indicative of incompleteness of the used optimality criterion, and therefore, instead of abandoning the optimality approach, it is more productive to focus on the identification of the important aspects of the entire behavioral paradigm in addition to the perceptual decision rule. Here, we will demonstrate that optimization of behavior as a whole accounts for the suboptimality of the decision rule on two examples discussed by the authors – namely, inter-observer/trial variability, while decision rule optimality is observed on average (sect. 3.1.2 and 3.2) and perceptual biases (sect. 3.8.1 and 3.8.4).
The inter-observer/trial variability can be explained as a result of overlooking important components of the optimality criterion. In particular, the cost of neural effort for information processing should be taken into account (Dounskaia & Shimansky Reference Dounskaia2016; Shimansky & Rand Reference Shimansky and Rand2013). Decision making is based on processing sensory information and integrating it with internal representations of past experience. These steps of information processing are required for estimating the state of the relevant constituents of the environment (perhaps including own body) to which the decision rule is applied. These steps are an essential component of the behavioral paradigm, and therefore, the cost of the corresponding neural effort needs to be included in the optimality criterion. In the field of movement control, where an optimality approach has successfully accounted for vast experimental data (for reviews, see Shimansky et al. Reference Shimansky, Kang and He2004; Todorov Reference Todorov2004), the consideration of the cost of information processing was critical for understanding even relatively simple motor behaviors such as reaching to grasp (Shimansky & Rand Reference Shimansky and Rand2013) and point-to-point movements (Rand & Shimansky Reference Rand and Shimansky2013). Also, the “trailing” pattern of joint coordination typically observed during well-learned arm movements can be fully understood only if neural effort for joint coordination is considered as a primary component of the optimality criterion (Dounskaia & Shimansky Reference Dounskaia2016; Goble et al. Reference Goble, Zhang, Shimansky, Sharma and Dounskaia2007).
The consideration of the cost of neural effort for information processing implies that the total cost function is a weighted sum of this cost and the cost of deviations from decision optimality. The brain is therefore required to perform a tradeoff between the two costs. Disregarding this tradeoff and focusing on decision optimality only would lead to a conclusion that experimentally observed decisions are suboptimal. However, deviations of the decisions from optimality are predicted by a tradeoff between the two costs: Decision optimality often requires a neural effort of excessive cost, thus making the total cost greater than optimal. Hence, perceptual decision suboptimality can be explained by applying an optimality approach to the entire behavior instead of to the decision rule only. Similar considerations were employed to explain the variability of hand motion during reach-to-grasp movements (Shimansky & Rand Reference Shimansky and Rand2013).
Experimentally observed perceptual biases may also be consistent with perceptual decision optimality. Shimansky (Reference Shimansky2011) used an optimality approach to predict perceptual biases in experimental conditions that included a combination of perceptual uncertainty with loss asymmetry with respect to the direction of decision error. An example can be jumping over an obstacle under poor visibility conditions. As Shimansky (Reference Shimansky2011) demonstrated, an optimality approach predicts a tendency to overestimate the size of the obstacle under these conditions.
In addition to suboptimality of experimentally observed perceptual decisions, another criticism of the optimality approach formulated by R&D is “flexibility” of the optimization criterion because of uncertainty about its exact composition. Similar arguments against the optimality approach were formulated in the field of movement control. Namely, it was noted that use of an optimality approach leads to “circulatory” reasoning, meaning that experimental data are used to determine the optimization criterion, and then the optimality approach is used for explaining the experimental results (e.g., Diedrichsen et al. Reference Diedrichsen, Shadmehr and Ivry2010). A solution to this seeming paradox has been proposed by Shimansky and Rand (Reference Shimansky and Rand2013). In brief, it consists of using a relatively small subset of the total amount of collected experimental data for determining unknown parameters of the optimality criterion (e.g., weights of the cost function components), with subsequent testing of the determined parameters on the rest of the experimental data. Although validity of this method of establishing the optimality criterion was demonstrated for data obtained in experiments on reach-to-grasp and point-to-point movements, this method can be extended to the field of perceptual decision making.
It is also noteworthy that even though R&D suggest abandoning the optimality approach, the specific hypotheses they formulate (their Table 1) are indirectly based on a certain model of optimal behavior. For example, the terms “corrupt,” “weird,” or “‘suboptimal behavior” (used in Table 1) make sense only with respect to a certain criterion of behavior optimality. Therefore, an optimality approach is needed to measure the extent of optimality and, in case of suboptimality, help identifying possible factors causing it.
In conclusion, the suboptimality of perceptual decisions described in the target article does not warrant abandoning the usage of an optimality approach. A more general form of optimality approach is required, where an assumption of optimality is applied to the entire paradigm instead of the decision rule alone, which would require use of a more complex form of cost function. Specific hypotheses regarding possible reasons for decision rule suboptimality could be formulated in terms of additional cost function components.
Use of an optimality approach has been remarkably successful in many different domains of the natural sciences. Its application to biological organisms equipped with a well-developed central nervous system (CNS) is generally based on the fact that these organisms learn, thus optimizing their behavior. Hence, a well-learned behavior can be considered optimized, and various features of such behavior can be explained as a result of optimization with respect to a specific criterion (also known as cost function). The explanatory power is perhaps the main advantage of an optimality approach. To fully benefit from that advantage, an optimality approach should be applied to the entire behavioral paradigm. However, the suggestion of Rahnev & Denison (R&D) to abandon the optimality approach is based on examples of suboptimality obtained through application of an optimality approach to the decision rule only. Here we argue that this suboptimality is indicative of incompleteness of the used optimality criterion, and therefore, instead of abandoning the optimality approach, it is more productive to focus on the identification of the important aspects of the entire behavioral paradigm in addition to the perceptual decision rule. Here, we will demonstrate that optimization of behavior as a whole accounts for the suboptimality of the decision rule on two examples discussed by the authors – namely, inter-observer/trial variability, while decision rule optimality is observed on average (sect. 3.1.2 and 3.2) and perceptual biases (sect. 3.8.1 and 3.8.4).
The inter-observer/trial variability can be explained as a result of overlooking important components of the optimality criterion. In particular, the cost of neural effort for information processing should be taken into account (Dounskaia & Shimansky Reference Dounskaia2016; Shimansky & Rand Reference Shimansky and Rand2013). Decision making is based on processing sensory information and integrating it with internal representations of past experience. These steps of information processing are required for estimating the state of the relevant constituents of the environment (perhaps including own body) to which the decision rule is applied. These steps are an essential component of the behavioral paradigm, and therefore, the cost of the corresponding neural effort needs to be included in the optimality criterion. In the field of movement control, where an optimality approach has successfully accounted for vast experimental data (for reviews, see Shimansky et al. Reference Shimansky, Kang and He2004; Todorov Reference Todorov2004), the consideration of the cost of information processing was critical for understanding even relatively simple motor behaviors such as reaching to grasp (Shimansky & Rand Reference Shimansky and Rand2013) and point-to-point movements (Rand & Shimansky Reference Rand and Shimansky2013). Also, the “trailing” pattern of joint coordination typically observed during well-learned arm movements can be fully understood only if neural effort for joint coordination is considered as a primary component of the optimality criterion (Dounskaia & Shimansky Reference Dounskaia2016; Goble et al. Reference Goble, Zhang, Shimansky, Sharma and Dounskaia2007).
The consideration of the cost of neural effort for information processing implies that the total cost function is a weighted sum of this cost and the cost of deviations from decision optimality. The brain is therefore required to perform a tradeoff between the two costs. Disregarding this tradeoff and focusing on decision optimality only would lead to a conclusion that experimentally observed decisions are suboptimal. However, deviations of the decisions from optimality are predicted by a tradeoff between the two costs: Decision optimality often requires a neural effort of excessive cost, thus making the total cost greater than optimal. Hence, perceptual decision suboptimality can be explained by applying an optimality approach to the entire behavior instead of to the decision rule only. Similar considerations were employed to explain the variability of hand motion during reach-to-grasp movements (Shimansky & Rand Reference Shimansky and Rand2013).
Experimentally observed perceptual biases may also be consistent with perceptual decision optimality. Shimansky (Reference Shimansky2011) used an optimality approach to predict perceptual biases in experimental conditions that included a combination of perceptual uncertainty with loss asymmetry with respect to the direction of decision error. An example can be jumping over an obstacle under poor visibility conditions. As Shimansky (Reference Shimansky2011) demonstrated, an optimality approach predicts a tendency to overestimate the size of the obstacle under these conditions.
In addition to suboptimality of experimentally observed perceptual decisions, another criticism of the optimality approach formulated by R&D is “flexibility” of the optimization criterion because of uncertainty about its exact composition. Similar arguments against the optimality approach were formulated in the field of movement control. Namely, it was noted that use of an optimality approach leads to “circulatory” reasoning, meaning that experimental data are used to determine the optimization criterion, and then the optimality approach is used for explaining the experimental results (e.g., Diedrichsen et al. Reference Diedrichsen, Shadmehr and Ivry2010). A solution to this seeming paradox has been proposed by Shimansky and Rand (Reference Shimansky and Rand2013). In brief, it consists of using a relatively small subset of the total amount of collected experimental data for determining unknown parameters of the optimality criterion (e.g., weights of the cost function components), with subsequent testing of the determined parameters on the rest of the experimental data. Although validity of this method of establishing the optimality criterion was demonstrated for data obtained in experiments on reach-to-grasp and point-to-point movements, this method can be extended to the field of perceptual decision making.
It is also noteworthy that even though R&D suggest abandoning the optimality approach, the specific hypotheses they formulate (their Table 1) are indirectly based on a certain model of optimal behavior. For example, the terms “corrupt,” “weird,” or “‘suboptimal behavior” (used in Table 1) make sense only with respect to a certain criterion of behavior optimality. Therefore, an optimality approach is needed to measure the extent of optimality and, in case of suboptimality, help identifying possible factors causing it.
In conclusion, the suboptimality of perceptual decisions described in the target article does not warrant abandoning the usage of an optimality approach. A more general form of optimality approach is required, where an assumption of optimality is applied to the entire paradigm instead of the decision rule alone, which would require use of a more complex form of cost function. Specific hypotheses regarding possible reasons for decision rule suboptimality could be formulated in terms of additional cost function components.