  For artificially intelligent learning systems to have widespread
applicability in real-world settings, it is important that they be able to
operate decentrally. Unfortunately, decentralized control is difficult --
computing even an epsilon-optimal joint policy is a NEXP complete problem.
Nevertheless, a recently rediscovered insight -- that a team of agents can
coordinate via common knowledge -- has given rise to algorithms capable of
finding optimal joint policies in small common-payoff games. The Bayesian
action decoder (BAD) leverages this insight and deep reinforcement learning to
scale to games as large as two-player Hanabi. However, the approximations it
uses to do so prevent it from discovering optimal joint policies even in games
small enough to brute force optimal solutions. This work proposes CAPI, a novel
algorithm which, like BAD, combines common knowledge with deep reinforcement
learning. However, unlike BAD, CAPI prioritizes the propensity to discover
optimal joint policies over scalability. While this choice precludes CAPI from
scaling to games as large as Hanabi, empirical results demonstrate that, on the
games to which CAPI does scale, it is capable of discovering optimal joint
policies even when other modern multi-agent reinforcement learning algorithms
are unable to do so. Code is available at https://github.com/ssokota/capi .
