RVσ(t): a unifying approach to performance and convergence in online multiagent learning

We present a new multiagent learning algorithm (<i>RV</i><inf>σ(<i>t</i>)</inf> that can guarantee both no-regret performance (all games) and policy convergence (some games of arbitrary size). Unlike its predecessor ReDVaLeR, it (1) does not need to distinguish whether its opponents are self-play or otherwise non-stationary, (2) is allowed to know its portion of <i>any</i> equilibrium that, we argue, leads to convergence in some games in addition to no-regret. Although the regret of <i>RV</i><inf>σ(<i>t</i>)</inf> is analyzed in continuous time, we show that it grows slower than in other no-regret techniques like GIGA and GIGA-WoLF. We show that <i>RV</i><inf>σ(<i>t</i>)</inf> can converge to coordinated behavior in coordination games, while GIGA, GIGA-WoLF may converge to poorly coordinated (mixed) behaviors.