Related papers: Accelerating Smooth Games by Manipulating Spectral…

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…

We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…

In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated…

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…

A central challenge in game theory and learning systems such as GANs is understanding which algorithms can efficiently compute equilibria across the heterogeneous landscape of games. Equilibrium computation is typically studied solver by…

We formulate an affine invariant implementation of the accelerated first-order algorithm in Nesterov (1983). Its complexity bound is proportional to an affine invariant regularity constant defined with respect to the Minkowski gauge of the…

We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective. This has opened up the possibility of introducing…

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the…

We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…

To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…

We study distributed optimization to minimize a global objective that is a sum of smooth and strongly-convex local cost functions. Recently, several algorithms over undirected and directed graphs have been proposed that use a gradient…

This work introduces a moving anchor acceleration technique to extragradient algorithms for smooth structured minimax problems. The moving anchor is introduced as a generalization of the original algorithmic anchoring framework, i.e. the…