OMWU achieves linear last-iterate convergence in KL divergence for unique interior Nash equilibria with optimal game-constant dependence due to quantified energy dissipation, while uniform best-iterate rates exhibit constant lower bounds in KL and TV but improved O(T^{-1/2}) duality-gap rates in 2x2
Thus fixing z⋆ ∈ argminz∈Z F(z) from Step (1), then also zτ = z⋆ + τJw ⋆ ∈ argminz∈Z F(z) for any τ ∈ R
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When and Why is Optimistic Multiplicative Weights Slow? The Geometry of Energy Dissipation
OMWU achieves linear last-iterate convergence in KL divergence for unique interior Nash equilibria with optimal game-constant dependence due to quantified energy dissipation, while uniform best-iterate rates exhibit constant lower bounds in KL and TV but improved O(T^{-1/2}) duality-gap rates in 2x2