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
Combining (106) from Step 2 and (107) from Step 3 yields ∥J∇F(z)∥2 z ≥ σ2 min · w2 min · (F(z) − F(z⋆))
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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