Related papers: Two-Player Games for Efficient Non-Convex Constrai…

The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…

Stochastic two-player games model systems with an environment that is both adversarial and stochastic. The adversarial part of the environment is modeled by a player (Player 2) who tries to prevent the system (Player 1) from achieving its…

In practice, many machine learning (ML) problems come with constraints, and their applied domains involve distributed sensitive data that cannot be shared with others, e.g., in healthcare. Collaborative learning in such practical scenarios…

The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex…

We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…

Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…

We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The theory is accomplished by introducing a new set-valued…

We consider a class of concave continuous games in which the corresponding admissible strategy profile of each player underlies affine coupling constraints. We propose a novel algorithm that leads the relevant population dynamic toward Nash…

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…

In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure…

Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al.…

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…