Optimal decision making with realistic bounds on neuronal activity

Many decision making models have been proposed to describe the neuronal activity in a two alternative choice paradigm. Due to evolutionary pressure, the values of the parameters of these models which maximize their accuracy are likely in biological decision networks. Such optimal parameters have been found for the linear versions of these models. However, in these linear models the firing rates of integrator neurons may achieve arbitrarily high and thus biologically unrealistic values. This paper analyses the one-dimensional Ornstein-Uhlenbeck (O-U) model with two types of restrictions on maximum firing rate proposed in the literature: reflecting and absorbing boundaries, which are able to confine the neural activity within certain interval and hence to make the original model more biologically realistic. We identify the optimal value of the linear parameter of the O-U model (typically denoted by lambda): it is positive for the model with reflecting boundaries and negative for the model with absorbing boundaries. Furthermore, both analytical and simulation results show that the two types of bounded O-U models hold close relationship and can achieve the same maximum accuracy under certain parameters. However, we claim that the decision network with absorbing boundaries is more energy efficient. Hence due to evolutionary pressure our analysis predicts that in biological decision networks, the maximum firing rate is more likely to be limited by absorbing rather than reflecting boundaries.