Feasibility of dopamine as a vector-valued feedback signal in the basal ganglia

It is well established that midbrain dopaminergic neurons support reinforcement learning (RL) in the basal ganglia by transmitting a reward prediction error (RPE) to the striatum. In particular, different computational models and experiments have shown that a striatum-wide RPE signal can support RL over a small discrete set of actions (e.g., no/no-go, choose left/right). However, there is accumulating evidence that the basal ganglia functions not as a selector between predefined actions but rather as a dynamical system with graded, continuous outputs. To reconcile this view with RL, there is a need to explain how dopamine could support learning of continuous outputs, rather than discrete action values. Inspired by the recent observations that besides RPE, the firing rates of midbrain dopaminergic neurons correlate with motor and cognitive variables, we propose a model in which dopamine signal in the striatum carries a vector-valued error feedback signal (a loss gradient) instead of a homogeneous scalar error (a loss). We implement a local, "three-factor" corticostriatal plasticity rule involving the presynaptic firing rate, a postsynaptic factor, and the unique dopamine concentration perceived by each striatal neuron. With this learning rule, we show that such a vector-valued feedback signal results in an increased capacity to learn a multidimensional series of real-valued outputs. Crucially, we demonstrate that this plasticity rule does not require precise nigrostriatal synapses but remains compatible with experimental observations of random placement of varicosities and diffuse volume transmission of dopamine.