We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best L-Lipschitz constan
t predictors. Then, we show why the obtained regret bound entails the asymptotical optimality with respect to the class of bounded stationary ergodic processes.
We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorith
m) with multiple learning rates. These bounds are in terms of excess losses, the differences between the instantaneous losses suffered by the algorithm and the ones of a given expert. We then demonstrate the interest of these bounds in the context of experts that report their confidences as a number in the interval [0,1] using a generic reduction to the standard setting. We conclude by two other applications in the standard setting, which improve the known bounds in case of small excess losses and show a bounded regret against i.i.d. sequences of losses.
We consider the setting of sequential prediction of arbitrary sequences based on specialized experts. We first provide a review of the relevant literature and present two theoretical contributions: a general analysis of the specialist aggregation rul
e of Freund et al. (1997) and an adaptation of fixed-share rules of Herbster and Warmuth (1998) in this setting. We then apply these rules to the sequential short-term (one-day-ahead) forecasting of electricity consumption; to do so, we consider two data sets, a Slovakian one and a French one, respectively concerned with hourly and half-hourly predictions. We follow a general methodology to perform the stated empirical studies and detail in particular tuning issues of the learning parameters. The introduced aggregation rules demonstrate an improved accuracy on the data sets at hand; the improvements lie in a reduced mean squared error but also in a more robust behavior with respect to large occasional errors.
