A parallel stochastic algorithm is investigated for error-descent learning and optimization in deterministic networks of arbitrary topology. No explicit information about internal network struc(cid:173) ture is needed. The method is based on the model-free distributed learning mechanism of Dembo and Kailath. A modified parameter update rule is proposed by which each individual parameter vector perturbation contributes a decrease in error. A substantially faster learning speed is hence allowed. Furthermore, the modified algo(cid:173) rithm supports learning time-varying features in dynamical net(cid:173) works. We analyze the convergence and scaling properties of the algorithm, and present simulation results for dynamic trajectory learning in recurrent networks.
1 Background and Motivation
We address general optimization tasks that require finding a set of constant param(cid:173) eter values Pi that minimize a given error functional £(p). For supervised learning, the error functional consists of some quantitative measure of the deviation between a desired state x T and the actual state of a network x, resulting from an input y and the parameters p. In such context the components of p consist of the con(cid:173) nection strengths, thresholds and other adjustable parameters in the network. A