Relax and Randomize : From Value to Algorithms

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones, also capturing such ''unorthodox'' methods as Follow the Perturbed Leader and the R 2 forecaster. Understanding the inherent complexity of the learning problem thus leads to the development of algorithms. To illustrate our approach, we present several new algorithms, including a family of randomized methods that use the idea of a ''random play out''.