Figure 4.
Cost of Control Applied to Drift Diffusion
(A) The drift-diffusion model assumes an accumulator integrating incoming information at a fixed drift rate (μ), subject to noise (σ), until it reaches a threshold (θ). The red line illustrates the trajectory in an example trial. Blue histograms indicate the distribution of response times for correct and incorrect responses. Increasing the threshold leads to more accurate decisions, at the cost of slower responses. In order to account for violations of the speed-accuracy trade-off, we introduced a costly noise-reduction parameter (uP), similar to our extended motor control model. This permits the optimal combination of threshold and precision to be chosen.
(B–E) Simulations provide reaction times and accuracy (i.e., when the decision terminates, and whether it is at the positive or negative boundary) for a variety of signal sizes (μ), noise (σ), and reward levels (R). For each condition, the optimal pairing of threshold (θ) and precision (uP) is selected to maximize value (EV). The value of a pair was calculated as accuracy multiplied by reward, temporally discounted by the reaction time.
(B and C) As reward increases, it is optimal to increase the precision and lower the decision threshold.
(D) This leads to improved accuracy with reward.
(E) When the signal-to-noise ratio is high, reward encourages faster responding; however, when the decision is noisy, reaction times actually increase with reward, despite falling thresholds—producing a speed-accuracy trade-off.