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Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…
We study the complexity of deciding the existence of mixed equilibria for minimization games where players use valuations other than expectation to evaluate their costs. We consider risk-averse players seeking to minimize the sum…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family.…
We present Coordinated Proximal Policy Optimization (CoPPO), an algorithm that extends the original Proximal Policy Optimization (PPO) to the multi-agent setting. The key idea lies in the coordinated adaptation of step size during the…
This paper deals with quasi-variational inequality problems (QVIs) in a generic Banach space setting. We provide a theoretical framework for the analysis of such problems which is based on two key properties: the pseudomonotonicity (in the…
We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…
A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
In this work, we analyse a simplified frictional contact problem and its variational formulation that has a form of the elliptic variational inequality of the second kind. For this problem, we consider a numerical approximation based on…
The classical convex feasibility problem in a finite dimensional Euclidean space is studied in the present paper. We are interested in two cases. First, we assume to know how to compute an exact project onto one of the sets involved and the…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…