However, one can do better if the problem is smooth (i.e., the gradient is Lipschitz). In this case, using two optimistic online learning algorithms, the convergence will be faster. Moreover, if you use optimistic online gradient descent/ascent, the last iterate will converge
Francesco Orabona@bremen79
If the problem is convex in the first variable and concave in the second one, we can use two online learning algorithms playing against each other. It is easy to show (e.g., see my online learning book) that the average of the iterates will converge to the saddle point.
8:06 AM · Jun 15, 2026 · 852 Views
