Better Loss Bounds For Mixable Games

Several algorithms for prediction with expert advice were designed to compete under the bounded and convex loss functions. Sometimes one can derive the better bounds for the mixable losses. It seems the importance of this question consists in the square-loss games, which can be often used in practice. The theoretical bounds are too big to compare them with the experimental performance of an algorithm. One of the algorithms that has such specific bound is Weighted Average Algorithm. The question is to derive the bounds for other ones, like Weak Aggregating Algorithm,Exponentiated Gradient, and may be even Gradient Descent.