Summary of Local Convergence Of Simultaneous Min-max Algorithms to Differential Equilibrium on Riemannian Manifold, by Sixin Zhang
Local convergence of simultaneous min-max algorithms to differential equilibrium on Riemannian manifold
by Sixin Zhang
First submitted to arxiv on: 22 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper studies min-max algorithms for solving zero-sum differential games on Riemannian manifolds. Building upon concepts like differential Stackelberg equilibrium and differential Nash equilibrium, the authors analyze the local convergence of two deterministic simultaneous algorithms, τ-GDA and τ-SGA, to these equilibria. They establish sufficient conditions for linear convergence rate using Ostrowski theorem and spectral analysis, and extend τ-SGA from the symplectic gradient-adjustment method in Euclidean space. The study shows that in some cases, τ-SGA can achieve a faster convergence rate to differential Stackelberg equilibrium compared to τ-GDA. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about using special kinds of computer algorithms to play games on curvy surfaces called Riemannian manifolds. The researchers looked at how these algorithms work and why they’re good or bad for solving certain types of problems. They found that some algorithms are better than others at reaching a special kind of balance in the game, which is important for training machines like artificial intelligence. |
