Optimistic no-regret learning converges pointwise to a Nash equilibrium in games with non-negative weighted regret, including harmonic games, when the equilibrium set is discrete.
Flows and decompositions of games: Harmonic and potential games
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Pointwise Convergence in Games with Conflicting Interest
Optimistic no-regret learning converges pointwise to a Nash equilibrium in games with non-negative weighted regret, including harmonic games, when the equilibrium set is discrete.