On the dual formulation of regularized linear systems with convex risks

In this paper, we study a general formulation of linear prediction algorith ms including a number of known methods as special cases. We describe a conv ex duality for this class of methods and propose numerical algorithms to so lve the derived dual learning problem. We show that the dual formulation is closely related to online learning algorithms. Furthermore, by using this duality, we show that new learning methods can be obtained. Numerical examp les will be given to illustrate various aspects of the newly proposed algor ithms.