Provable local learning rule by expert aggregation for a Hawkes network

We propose a simple network of Hawkes processes as a cognitive model capable of learning to classify objects. Our learning algorithm, named EWAK for Exponentially Weighted Average and Kalikow decomposition, is based on a local synaptic learning rule based on firing rates at each output node. We were able to use local regret bounds to prove mathematically that the network is able to learn on average and even asymptotically under more restrictive assumptions.