Your formulation does not look even close to the image. It seems to correspond to the optimization problem at How can i solve the min-max convex optimization question . which is a different problem.
I can’t tell you what the correct formulations is, for the problem in the image (in your question in this thread) or even whether the problem is convex, because I have no idea what a(theta) or G_d(theta)` are. Do you know what they are? Have you proven the problem is convex? The convexity of the objective looks rather dubious.