Maximizing reinforcement rate on spaced-responding schedules under conditions of temporal uncertainty.

The problem of finding the response strategy that maximizes reinforcement rate under differential-reinforcement-of low-rate (DRL) schedules, when emitted inter-response-time (IRT) distributions have some variance, is considered. In general, if IRT distributions are generated so that their standard deviation remains a constant fraction of the mean IRT, then linear overestimation of the DRL schedule value is the optimal strategy, with the degree of overestimation which is optimal depending on the degree of temporal uncertainty, but generally being in the region of 10-20%. If the mean of emitted IRT distributions underestimates the schedule value, the reinforcement rate obtained is below maximal, and increases in IRT distribution variability actually increase obtained reinforcement rate. Thus, in conditions in which underestimation is forced, the DRL schedule may discourage accurately-regulated timing. Various satisficing policies producing 25, 50, and 75% of the maximum obtainable reinforcement rate) will lead to linear underestimation of the schedule value. Experimental data showing both linear over- and under-estimation can be found in the experimental literature. In general, therefore, deviations from accurate timing of behaviour on DRL schedules may not be the result of inaccuracies of underlying timing processes, but may occur because of maximizing or satisficing reinforcement rate.