Competitive Gradient Optimization
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Abstract (arXiv)
We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of α-coherent function for which we provide convergence analysis. We show that for strictly α-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in α-coherent class of functions.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 25 of its 45 references that are in the map. First posted on arXiv 27 May 2022.
Builds on
25 of 45 references.
References · 25
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13 more
- 2015Online Optimization : Competing with Dynamic Comparatorscited by 99
- 2018The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimizationcited by 98
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- 2020Competitive Policy Optimizationcited by 6
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Citing papers per year: 2023: 1.
1 paper.