RESUMO
We study online nonlinear learning over distributed multiagent systems, where each agent employs a single hidden layer feedforward neural network (SLFN) structure to sequentially minimize arbitrary loss functions. In particular, each agent trains its own SLFN using only the data that is revealed to itself. On the other hand, the aim of the multiagent system is to train the SLFN at each agent as well as the optimal centralized batch SLFN that has access to all the data, by exchanging information between neighboring agents. We address this problem by introducing a distributed subgradient-based extreme learning machine algorithm. The proposed algorithm provides guaranteed upper bounds on the performance of the SLFN at each agent and shows that each of these individual SLFNs asymptotically achieves the performance of the optimal centralized batch SLFN. Our performance guarantees explicitly distinguish the effects of data- and network-dependent parameters on the convergence rate of the proposed algorithm. The experimental results illustrate that the proposed algorithm achieves the oracle performance significantly faster than the state-of-the-art methods in the machine learning and signal processing literature. Hence, the proposed method is highly appealing for the applications involving big data.
RESUMO
We study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance.
