LETTER Communicated by Gal Chechik Reinforcement Learning Through Modulation of Spike-Timing-Dependent Synaptic Plasticity

The persistent modification of synaptic efficacy as a function of the rela-tive timing of pre- and postsynaptic spikes is a phenomenon known as spike-timing-dependent plasticity (STDP). Here we show that themodu-lation of STDP by a global reward signal leads to reinforcement learning. We first derive analytically learning rules involving reward-modulated spike-timing-dependent synaptic and intrinsic plasticity, by applying a reinforcement learning algorithm to the stochastic spike response model of spiking neurons. These rules have several features common to plastic-ity mechanisms experimentally found in the brain. We then demonstrate in simulations of networks of integrate-and-fire neurons the efficacy of two simple learning rules involving modulated STDP. One rule is a di-rect extension of the standard STDP model (modulated STDP), and the other one involves an eligibility trace stored at each synapse that keeps a decaying memory of the relationships between the recent pairs of pre-and postsynaptic spike pairs (modulated STDP with eligibility trace). This latter rule permits learning even if the reward signal is delayed. The proposed rules are able to solve the XOR problem with both rate-coded and temporally coded input and to learn a target output firing-rate pattern. These learning rules are biologically plausible, may be used for training generic artificial spiking neural networks, regardless of the neu-ral model used, and suggest the experimental investigation in animals of the existence of reward-modulated STDP.