  We consider an online load balancing problem and its extensions in the
framework of repeated games. On each round, the player chooses a distribution
(task allocation) over $K$ servers, and then the environment reveals the load
of each server, which determines the computation time of each server for
processing the task assigned. After all rounds, the cost of the player is
measured by some norm of the cumulative computation-time vector. The cost is
the makespan if the norm is $L_\infty$-norm. The goal is to minimize the
regret, i.e., minimizing the player's cost relative to the cost of the best
fixed distribution in hindsight. We propose algorithms for general norms and
prove their regret bounds. In particular, for $L_\infty$-norm, our regret bound
matches the best known bound and the proposed algorithm runs in polynomial time
per trial involving linear programming and second order programming, whereas no
polynomial time algorithm was previously known to achieve the bound.
