multiple agents. In this article, we consider the game-theoretic concept of regret as a stand-in for the optimality criteria of the single-agent work. As with the inverse optimal control problem, the result is fundamentally ill-posed. We address this by requiring that for any utility function linear in known features, our learned model must have no more regret than that of the observed behavior. We demonstrate that this requirement can be re-cast as a set of equivalent convex constraints that we denote the [*inverse correlated equilibrium*]{} (ICE) polytope.

As we are interested in the effective prediction of behavior, we will use a maximum entropy criteria to select behavior from this polytope. We demonstrate that optimizing this criteria leads to mini-max optimal prediction of behavior subject to approximate rationality. We consider the dual of this problem and note that it generalizes the traditional log-linear maximum entropy family of problems [@della2002inducing]. We provide a simple and computationally efficient gradient-based optimization strategy for this family and show that only a small number of observations are required for accurate prediction and transfer of behavior. We conclude by considering a variety of experimental results, ranging from predicting travel routes in a synthetic routing game to a 