Competitive Gradient Optimization

arXiv2205.14232MaRDI QIDQ6400397

Author name not available (Why is that?)

Publication date: 27 May 2022

Abstract: 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 $alpha$-coherent function for which we provide convergence analysis. We show that for strictly $alpha$-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 $alpha$-coherent class of functions.

Has companion code repository: https://github.com/abhijeetiitmvyas/competitivegradientoptim

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