text: 292,151,1309300896208171009,734677275216470016,Guodong Zhang,"New paper alert: <LINK> We provide a unified and automated method to analyze first-order methods for smooth & strongly-monotone games. The convergence rate for any first-order method can be obtained via a mechanical procedure of deriving and solving an SDP. <LINK> Using this framework, we are able to recover or even improve known convergence bounds for a variety of algorithms. For example, we can recover the rate bound of the gradient method, proximal point method, and optimistic gradient method. We can also gain new insights and derive new results that were previously unknown. For example, we for the first time provide the global convergence result of negative momentum, which is difficult to obtain using existing approaches. Finally, we are able to extend this framework to a stochastic setting with multiplicative noise. See more details in the paper. Joint work with @XuchanB, @LaurentLessard and @RogerGrosse .",https://arxiv.org/abs/2009.11359,"The theory of integral quadratic constraints (IQCs) allows the certification of exponential convergence of interconnected systems containing nonlinear or uncertain elements. In this work, we adapt the IQC theory to study first-order methods for smooth and strongly-monotone games and show how to design tailored quadratic constraints to get tight upper bounds of convergence rates. Using this framework, we recover the existing bound for the gradient method~(GD), derive sharper bounds for the proximal point method~(PPM) and optimistic gradient method~(OG), and provide \emph{for the first time} a global convergence rate for the negative momentum method~(NM) with an iteration complexity $\mathcal{O}(\kappa^{1.5})$, which matches its known lower bound. In addition, for time-varying systems, we prove that the gradient method with optimal step size achieves the fastest provable worst-case convergence rate with quadratic Lyapunov functions. Finally, we further extend our analysis to stochastic games and study the impact of multiplicative noise on different algorithms. We show that it is impossible for an algorithm with one step of memory to achieve acceleration if it only queries the gradient once per batch (in contrast with the stochastic strongly-convex optimization setting, where such acceleration has been demonstrated). However, we exhibit an algorithm which achieves acceleration with two gradient queries per batch. ","A Unified Analysis of First-Order Methods for Smooth Games via Integral