  Counterfactual regret minimization (CFR) is a family of iterative algorithms
that are the most popular and, in practice, fastest approach to approximately
solving large imperfect-information games. In this paper we introduce novel CFR
variants that 1) discount regrets from earlier iterations in various ways (in
some cases differently for positive and negative regrets), 2) reweight
iterations in various ways to obtain the output strategies, 3) use a
non-standard regret minimizer and/or 4) leverage "optimistic regret matching".
They lead to dramatically improved performance in many settings. For one, we
introduce a variant that outperforms CFR+, the prior state-of-the-art
algorithm, in every game tested, including large-scale realistic settings. CFR+
is a formidable benchmark: no other algorithm has been able to outperform it.
Finally, we show that, unlike CFR+, many of the important new variants are
compatible with modern imperfect-information-game pruning techniques and one is
also compatible with sampling in the game tree.
