13.3 Maximum conditional Maxent. An alternative measure of closeness, instead of the conditional relative entropy, is the maximum relative entropy over all x 2 X1.

(a) Write the primal optimization problem for this maximum conditional Maxent formulation. Show that it is a convex optimization problem, and discuss its feasibility and the uniqueness of its solution.

(b) Prove a duality theorem for maximum conditional Maxent and write the equivalent dual problem.

(c) Analyze the properties of maximum conditional Maxent and give a generalization bound for the algorithm.