Learned helplessness experiments involving controllable vs. uncontrollable stressors have shown that
the perceived ability to control events has profound consequences for decision making. Normative models of decision making, however, do not naturally incorporate knowledge about controllability, and previous approaches to incorporating it have led to solutions with biologically implausible computational demands [1,2]. Intuitively, controllability bounds the differential rewards for choosing one strategy over another, and therefore believing that the environment is uncontrollable should reduce one’s willingness to invest time and effort into choosing between options. Here, we offer a normative, resource-rational account of the role of controllability in trading mental effort for expected gain. In this view, the brain not only faces the task of solving Markov decision problems (MDPs), but it also has to optimally allocate its finite computational resources to solve them efficiently. This joint problem can itself be cast as a MDP , and its optimal solution respects computational constraints by design.
We start with an analytic characterisation of the influence of controllability on the use of computational
resources. We then replicate previous results on the effects of controllability on the differential value
of exploration vs. exploitation, showing that these are also seen in a cognitively plausible regime of
computational complexity. Third, we find that controllability makes computation valuable, so that it is
worth investing more mental effort the higher the subjective controllability. Fourth, we show that in this
model the perceived lack of control (helplessness) replicates empirical findings  whereby patients
with major depressive disorder are less likely to repeat a choice that led to a reward, or to avoid a choice that led to a loss. Finally, the model makes empirically testable predictions about the relationship between reaction time and helplessness.