  This thesis presents some geometric insights into three different types of
two player prediction games -- namely general learning task, prediction with
expert advice, and online convex optimization. These games differ in the nature
of the opponent (stochastic, adversarial, or intermediate), the order of the
players' move, and the utility function. The insights shed some light on the
understanding of the intrinsic barriers of the prediction problems and the
design of computationally efficient learning algorithms with strong theoretical
guarantees (such as generalizability, statistical consistency, and constant
regret etc.).
