Fig 1.
Hierarchical and parallel planning processes.
A. A simple maze where selecting the initial direction of a best goal-reaching path benefits from the joint consideration of starting-point proximal (myopic) and goal-proximal (future) information. B. The task in A. embedded as an initial part of a larger maze. C. A hierarchical approach to selecting the initial path in B., by first reducing the task to the initial subgoal task then focusing on finding the best subgoal-reaching path. D. A parallel approach to selecting the initial path in B., where simultaneous but appropriately-weighted consideration of constraints both inside and outside of the subtask context generates approximately optimal choice behavior.
Fig 2.
Blue block: starting point. Starred red block: goal location. Trial advantage types are based on the correspondence between the starting-point proximal constraint (myopic advantage) and the goal-/subgoal-proximal constraint (future advantage). NT = neutral advantage, SA = single advantage, CA = congruent advantage, IA = incongruent advantage. For the subgoal trials in Experiment 2, both of the possible final goal locations are shown.
Table 1.
Myopic and future path advantages.
All trial layouts were mirrored except for the NT trial. NT = neutral advantage, SA = single advantage, CA = congruent advantage, IA = incongruent advantage. The -m and -f suffixes indicate whether the myopic or future advantage was larger.
Fig 3.
Initial path choices and the associated response times reflected joint consideration of myopic and future constraints.
A. Path choices in trials with equally optimal initial directions. The value for NT trials was defined to be 0 since there was neither a myopic nor a future advantage on these trials. B. Path choices in trials where one of the initial directions was optimal. The proportion of optimal trials for each individual was converted into a probit score. If the individual probit score was larger than 3 or smaller than -3, it was capped at 3 or -3 before averaging. C. Response times associated with the first step. The individual medians of zscored response times were projected back to the raw time scale in seconds using group average mean response times and group average standard deviations. Trial advantage types: NT = neutral advantage, SA = single advantage, CA = congruent advantage, IA = incongruent advantage. mAdv = myopic advantage. -m and -f indicates the larger advantage. Error bars indicate bootstrapped 95% confidence limits.
Fig 4.
Weighted integration of myopic and future constraints in initial-step decision making in the base task.
A. Test data objective (summed negative log-likelihood) of candidate drift-diffusion models, as marked on dark red bars, as compared to the baseline model (see text for details). Asterisk marks the winning model. B. Parameter estimates of the winning drift-diffusion model. t0, non-decision time. a, decision bound. md and fd, myopic and future advantage weights. sz, inter-trial variability of the starting point. sd, inter-trial variability of the drift rate. C. Predicted response time (RT) distributions (in red, sampled from the parameter estimates of the winning fit in the fold with the best test objective) and the empirical RT distributions (in blue). In C., the top two panels show the RT distributions associated with choices satisfying the myopic advantage on the top and those satisfying the future advantage on the bottom. The bottom four panels show the RT distributions for the correct responses on the top and error responses on the bottom. mAdv, myopic advantage. fAdv, future advantage. All error bars indicate 95% bootstrapped confidence limits.
Fig 5.
Accuracy and time cost in initial path choices when the two-constraint maze is embedded as a subtask.
A. Path selection in the trials with equally optimal initial directions. As in Fig 3A, the value for NT trials was defined to be 0. B. Path selection across advantage pairings in base and subgoal trials. As in Fig 3B, the proportion of optimal trials for each individual was converted into a probit score, with individual probit scores larger than 3 or smaller than -3 capped at 3 or -3 before averaging. C. Response times in the base and subgoal trials. As in Fig 3C, the median zscore response times were projected back to the raw time scale in seconds.
Fig 6.
Weighted consideration of subgoal-relevant and -irrelevant constraints approximated optimal choice behavior when the base task was embedded as an initial subgoal task.
A. Path choices in the IA trials. As in Figs 3B and 5B, the proportion of optimal trials for each individual was converted into a probit score, with individual probit scores larger than 3 or smaller than -3 capped at 3 or -3 before averaging. B. Test data objective (summed negative log-likelihood) of the candidate drift-diffusion models compared to the baseline model. Asterisk marks the winning model. For empirical and predicted response time distributions, see S4 Fig. C. Parameter estimates from the winning model. t0, non-decision time. a, decision bound. md and fd, myopic and future advantage weights. gd, goal weight. sz, inter-trial variability of the starting point. sd, inter-trial variability of the drift rate. p, proportional change to md and fd in the subgoal trials.
Fig 7.
Individual differences in weighting subgoal-relevant factors and the subgoal-irrelevant final goal.
A. and B. Subgoal trial path choices associated with the two accuracy groups. As in Fig 6A, the proportion of optimal trials for each individual was converted into a probit score, with individual probit scores larger than 3 or smaller than -3 capped at 3 or -3 before averaging. C. Drift weight estimates in both task conditions for the two accuracy groups.