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Under mild regularity conditions, gradient-based methods converge globally to a critical point in the single-loss setting.
Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
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Algorithms in Real Algebraic Geometry
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Multiplicative weights update with constant step-size in congestion games: Convergence, limit cycles and chaos
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Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions
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On finding local nash equilibria (and only local nash equilibria) in zero-sum games
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Poincaré recurrence, cycles and spurious equilibria in gradient-descent-ascent for non-convex non-concave zero-sum games
Emmanouil-Vasileios Vlatakis-Gkaragkounis, Lampros Flokas, and Georgios Piliouras · 2019
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Policy optimization provably converges to nash equilibria in zero-sum linear quadratic games
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Policy-gradient algorithms have no guarantees of convergence in linear quadratic games
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