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Competitive Gradient Descent
Florian Schaefer · Anima Anandkumar

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #195

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on \emph{optimism} and \emph{consensus} and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations.

Author Information

Florian Schaefer (Caltech)
Anima Anandkumar (NVIDIA / Caltech)

Anima Anandkumar is a Bren professor at Caltech CMS department and a director of machine learning research at NVIDIA. Her research spans both theoretical and practical aspects of large-scale machine learning. In particular, she has spearheaded research in tensor-algebraic methods, non-convex optimization, probabilistic models and deep learning. Anima is the recipient of several awards and honors such as the Bren named chair professorship at Caltech, Alfred. P. Sloan Fellowship, Young investigator awards from the Air Force and Army research offices, Faculty fellowships from Microsoft, Google and Adobe, and several best paper awards. Anima received her B.Tech in Electrical Engineering from IIT Madras in 2004 and her PhD from Cornell University in 2009. She was a postdoctoral researcher at MIT from 2009 to 2010, a visiting researcher at Microsoft Research New England in 2012 and 2014, an assistant professor at U.C. Irvine between 2010 and 2016, an associate professor at U.C. Irvine between 2016 and 2017 and a principal scientist at Amazon Web Services between 2016 and 2018.

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