  We develop new parameter-free and scale-free algorithms for solving
convex-concave saddle-point problems. Our results are based on a new simple
regret minimizer, the Conic Blackwell Algorithm$^+$ (CBA$^+$), which attains
$O(1/\sqrt{T})$ average regret. Intuitively, our approach generalizes to other
decision sets of interest ideas from the Counterfactual Regret minimization
(CFR$^+$) algorithm, which has very strong practical performance for solving
sequential games on simplexes. We show how to implement CBA$^+$ for the
simplex, $\ell_{p}$ norm balls, and ellipsoidal confidence regions in the
simplex, and we present numerical experiments for solving matrix games and
distributionally robust optimization problems. Our empirical results show that
CBA$^+$ is a simple algorithm that outperforms state-of-the-art methods on
synthetic data and real data instances, without the need for any choice of step
sizes or other algorithmic parameters.
