2 research outputs found
Last Round Convergence and No-Instant Regret in Repeated Games with Asymmetric Information
This paper considers repeated games in which one player has more information
about the game than the other players. In particular, we investigate repeated
two-player zero-sum games where only the column player knows the payoff matrix
A of the game. Suppose that while repeatedly playing this game, the row player
chooses her strategy at each round by using a no-regret algorithm to minimize
her (pseudo) regret. We develop a no-instant-regret algorithm for the column
player to exhibit last round convergence to a minimax equilibrium. We show that
our algorithm is efficient against a large set of popular no-regret algorithms
of the row player, including the multiplicative weight update algorithm, the
online mirror descent method/follow-the-regularized-leader, the linear
multiplicative weight update algorithm, and the optimistic multiplicative
weight update
Online Double Oracle
Solving strategic games with huge action space is a critical yet
under-explored topic in economics, operations research and artificial
intelligence. This paper proposes new learning algorithms for solving
two-player zero-sum normal-form games where the number of pure strategies is
prohibitively large. Specifically, we combine no-regret analysis from online
learning with Double Oracle (DO) methods from game theory. Our method --
\emph{Online Double Oracle (ODO)} -- is provably convergent to a Nash
equilibrium (NE). Most importantly, unlike normal DO methods, ODO is
\emph{rationale} in the sense that each agent in ODO can exploit strategic
adversary with a regret bound of where is
not the total number of pure strategies, but rather the size of \emph{effective
strategy set} that is linearly dependent on the support size of the NE. On tens
of different real-world games, ODO outperforms DO, PSRO methods, and no-regret
algorithms such as Multiplicative Weight Update by a significant margin, both
in terms of convergence rate to a NE and average payoff against strategic
adversaries.Comment: [email protected]