Optimality and Some of Its Discontents: Successes and Shortcomings of Existing Models for Binary Decisions

Abstract

We review how leaky competing accumulators (LCAs) can be used to model decision making in two-alternative, forced-choice tasks, and we show how they reduce to drift diffusion (DD) processes in special cases. As continuum limits of the sequential probability ratio test, DD processes are optimal in producing decisions of specified accuracy in the shortest possible time. Furthermore, the DD model can be used to derive a speed-accuracy trade-off that optimizes reward rate for a restricted class of two alternative forced-choice decision tasks. We review findings that compare human performance with this benchmark, and we reveal both approximations to and deviations from optimality. We then discuss three potential sources of deviations from optimality at the psychological level-avoidance of errors, poor time estimation, and minimization of the cost of control-and review recent theoretical and empirical findings that address these possibilities. We also discuss the role of cognitive control in changing environments and in modulating exploitation and exploration. Finally, we consider physiological factors in which nonlinear dynamics may also contribute to deviations from optimality.

Deciding How To Decide: Self-Control and Meta-Decision Making

“…Adopting as an illustration the widespread view that the brain houses (at least) two distinct decision controllers (e.g., [4,11]), meta-optimization entails choices such as selecting the controller that performs the optimization and allocating to it resources such as time [12][13][14], then selecting the final outcome according to the preferences of that controller.…”

“…Thus, the decision is not only over the possible outcomes but also over the nuts and bolts of the internal decision processes themselves (or, 'setting the switches' [10]). We suggest that some simple mechanisms and decision variables may be widely shared across these domains.Adopting as an illustration the widespread view that the brain houses (at least) two distinct decision controllers (e.g., [4,11]), meta-optimization entails choices such as selecting the controller that performs the optimization and allocating to it resources such as time [12][13][14], then selecting the final outcome according to the preferences of that controller. …”

Inhibition and excitation shape activity selection: effect of oscillations in a decision-making circuit

“…A specific feature of diffusion models is their ability to resemble 8 statistically optimal processes [15]. However, it has been found that decision-makers do 9 not always behave optimally [2,8,[16][17][18]. Suboptimality may arise from the evolution of 10 decision rules in complex environments [2,16], from limited precision in neural 11 computations [18], or from nonlinearity in the neural network circuitry, as nonlinear 12 models often have several stable stationary states and therefore may integrate evidence 13 by reaching a decision state, which may not correspond to the optimal solution [8].14 The aim of the present paper is to study the behaviour of a hypothetical animal 15 performing ongoing activity selection through a nonlinear neural circuit model that 16 implements the interneuronal inhibitory motif.…”

Effect of Interactions between Harvester Ants on Forager Decisions

“…Sequential sampling models can capture trends for both response time and accuracy in two-choice decision tasks (Ratcliff and Rouder, 1998; Ratcliff and Smith, 2004; Bogacz et al, 2006). Sequential sampling models also can be related to optimal decision making strategies (e.g., Bogacz et al, 2006; Marshall et al, 2009; Brunton et al, 2013; Holmes and Cohen, 2014). Here we do not attempt to define an “optimal” response at the single-ant level.…”

“…This work contributes to the study of a fundamental problem in behavior, how individual decisions are made based on noisy evidence (Smith and Ratcliff, 2004; Bogacz et al, 2006; Holmes and Cohen, 2014). Many decisions are made by accumulating evidence to a threshold.…”