  Counterfactual Regret Minimization (CFR) has found success in settings like
poker which have both terminal states and perfect recall. We seek to understand
how to relax these requirements. As a first step, we introduce a simple
algorithm, local no-regret learning (LONR), which uses a Q-learning-like update
rule to allow learning without terminal states or perfect recall. We prove its
convergence for the basic case of MDPs (and limited extensions of them) and
present empirical results showing that it achieves last iterate convergence in
a number of settings, most notably NoSDE games, a class of Markov games
specifically designed to be challenging to learn where no prior algorithm is
known to achieve convergence to a stationary equilibrium even on average.
