On the Value of Stochastic Side Information in Online Learning

As a common situation in practice, the forecaster could access some additional resources which we call it side information, We study the effectiveness of stochastic side information in deterministic that may provide some useful knowledge on the online learning scenarios. We propose a forecaster sequence of interest. Cover and Ordentlich [10] first studied to predict a deterministic sequence where its performance is a portfolio investment problem where the sequence of interest evaluated against an expert class. We assume that certain is the stock vectors that may depend on some finite-valued stochastic side information is available to the forecaster but states (as side information), and their proposed forecaster can not the experts. We define the minimax expected regret for achieve the same wealth as the best side information dependent evaluating the forecaster's performance, for which we obtain investment strategy. Xie and Barron [11] studied the case when both upper and lower bounds. Consequently, our results characterize the sequence of interest is generated according to a pair-wise the improvement in the regret due to the stochastic parametric distribution conditioning on the side information, side information. Compared with the classical online learning and derived an logarithmic upper bound of the minimax regret.