A Practical No-Linear-Regret Algorithm for Convex Games

For convex games, connections between playing by no-regret algorithms and playing equilibrium strategies have previously been made for Φregret, a generalization of external regret [5]. In particular, Gordon et al. present a no-Φ-regret algorithm for several different classes of transformations Φ [4]. In this paper, we instantiate the algorithm for the class of linear transformations using a variety of optimization techniques and give experimental results on several games including Indian poker, a simple but substantially large-scale variant of poker. Our results show that both no-external-regret and no-linear-regret algorithms can achieve better regret performances than what the current theory guarantees. To the best of our knowledge, this is the first work empirically demonstrating the benefits of a no-Φ-regret algorithm for general convex games where Φ is stronger than external.