Optimal policy for multi-alternative decisions

Every-day decisions frequently require choosing among multiple alternatives. Yet, the optimal policy for such decisions is unknown. Here we derive the normative policy for general multi-alternative decisions. This strategy requires evidence accumulation to nonlinear, time-dependent bounds, that trigger choices. A geometric symmetry in those boundaries allows the optimal strategy to be implemented by a simple neural circuit involving a normalization with fixed decision bounds and an urgency signal. The model captures several key features of the response of decision-making neurons as well as the increase in reaction time as a function of the number of alternatives, known as Hick's law. In addition, we show that, in the presence of divisive normalization and internal variability, our model can account for several so called ‘irrational' behaviors such as the similarity effect as well as the violation of both the independent irrelevant alternative principle and the regularity principle

Probabilistic decision making with spikes: From ISI distributions to behaviour via information gain

Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks