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About this paper
Jing An, Jianfeng Lu
Researchers at Duke University quantitatively characterize the convergence of two-timescale gradient descent-ascent dynamics, showing exponential rates for finite-dimensional quadratic games and Wasserstein-1 convergence for mean-field problems with locally non-convex objectives.
Key insights
- The convergence rate of continuous-time two-timescale GDA for finite-dimensional quadratic games is maximized when the learning rate ratio "eta" is of order 1.
- Mean-field GDA can achieve exponential Wasserstein-1 convergence to mixed Nash equilibria even when objective functions are locally non-convex/non-concave, provided strong convexity-concavity holds outside a local ball and entropy regularization is sufficient.
- Preconditioning discrete GDA updates can effectively mitigate numerical instability and slow convergence caused by extreme learning rate ratios, allowing for larger, more stable step sizes in practical implementations.
Summary by alphaXiv.
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