A Local Regret in Nonconvex Online Learning

We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models even in offline settings. Hence, gradient based definition of regrets are common for both offline and online nonconvex problems. Recently, a notion of local gradient based regret was introduced. Inspired by the concept of calibration and a local gradient based regret, we introduce another definition of regret and we discuss why our definition is more interpretable for forecasting problems. We also provide bound analysis for our regret under certain assumptions.Comment: Continual Workshop at NIPS 2018, 2 figures, 9 page

RNN-based Online Learning: An Efficient First-Order Optimization Algorithm with a Convergence Guarantee

We investigate online nonlinear regression with continually running recurrent neural network networks (RNNs), i.e., RNN-based online learning. For RNN-based online learning, we introduce an efficient first-order training algorithm that theoretically guarantees to converge to the optimum network parameters. Our algorithm is truly online such that it does not make any assumption on the learning environment to guarantee convergence. Through numerical simulations, we verify our theoretical results and illustrate significant performance improvements achieved by our algorithm with respect to the state-of-the-art RNN training methods.Comment: This paper was an early draft of the presented results. We have written and published another paper (arXiv:2005.08948) where we have improved the material in this paper. The published paper covers most of the material presented in this paper as well. Therefore, we remove this paper from Arxiv and kindly refer the interested readers to arXiv:2005.0894