Online optimization algorithms

This project surveys some recent algorithms and results in the field of online learning theory [5][6][7]. The problem context is that of an online decision problem, where one must choose a point xt from a fixed set K for each round t. After a choice has been made, a cost function ft(x) for that round is revealed and used to compute the cost of that decision. On the next round t + 1, a new point xt+1 must be chosen, a new cost function ft+1(x) will be revealed, and so on. The goal then is to minimize the regret R, the difference between the cumulative cost of the single best point chosen in hindsight x and the cumulative cost of the sequence of points chosen by the online procedure x1...T .