Lipschitzness, which we make precise in Section 2 and in Assumption 3.1.

Our preliminary results suggest that the regularized exponential mechanism can effectively emulate previous empirical and population risk bounds, negating the need for smoothness assumptions for algorithms with polynomial running time.

However, this assumption can possibly fail in real-world scenarios.

Consequently, standard online convex optimization algorithms do not directly apply.

However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances [34] on fast convergence in games are limited to no-regret algorithms such as online mirror descent, which satisfy stability.