We present new Multiagent learning (MAL) algorithms with the general philosophy of policy convergence against some classes of opponents but otherwise ensuring high payoffs. We consider a 3-class breakdown of opponent types: (eventually) stationary, self-play and "other" (see Definition 4) agents. We start with ReDVaLeR that can satisfy policy convergence against the first two types and no-regret against the third, but it needs to know the type of the opponents. This serves as a baseline to delineate the difficulty of achieving these goals. We show that a simple modification on ReDVaLeR yields a new algorithm, RV σ(t), that achieves no-regret payoffs in all games, and convergence to Nash equilibria in self-play (and to best response against eventually stationary opponents-a corollary of no-regret) simultaneously, without knowing the opponent types, but in a smaller class of games than ReDVaLeR . RV σ(t) effectively ensures the performance of a learner during the process of learning, as opposed to the performance of a learned behavior. We show that the expression for regret of RV σ(t) can have a slightly better form than those of other comparable algorithms like GIGA and GIGA-WoLF though, contrastingly, our analysis is in continuous time. Moreover, experiments show that RV σ(t) can converge to an equilibrium in some cases where GIGA, GIGA-WoLF would fail, and to better equilibria where GIGA, GIGA-WoLF converge to undesirable equilibria (coordination games). This important class of coordination games also highlights the key desirability of policy convergence as a criterion for MAL in self-play instead of high average payoffs. To our knowledge, this is also the first successful (guaranteed) attempt at policy convergence of a no-regret algorithm in the Shapley game.
- Game theory
- Multiagent reinforcement learning