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Convergence without Convexity: Sampling, Optimization, and Games

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Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

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This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...

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Global Convergence and Variance Reduction for a Class of Nonconvex-Nonconcave Minimax Problems

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Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice for solving these ...

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A Catalyst Framework for Minimax Optimization

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We introduce a generic two-loop scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated dual problem and takes full advantage of existing ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2020

A Catalyst Framework for Minimax Optimization

Negar Kiyavash

We introduce a generic \emph{two-loop} scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated \emph{dual problem} and takes full advantag ...

2020

Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees

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Developing classification algorithms that are fair with respect to sensitive attributes of the data is an important problem due to the increased deployment of classification algorithms in societal contexts. Several recent works have focused on studying cla ...

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Robust Adaptive Decision Making: Bayesian Optimization and Beyond

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The central task in many interactive machine learning systems can be formalized as the sequential optimization of a black-box function. Bayesian optimization (BO) is a powerful model-based framework for \emph{adaptive} experimentation, where the primary go ...

EPFL2019

Sampling can be faster than optimization

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Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...

PNAS2019

Scalable Convex Optimization Methods for Semidefinite Programming

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With the ever-growing data sizes along with the increasing complexity of the modern problem formulations, contemporary applications in science and engineering impose heavy computational and storage burdens on the optimization algorithms. As a result, there ...

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Learning Generalized Nash Equilibria in a Class of Convex Games

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We consider multiagent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we propose a novel dis ...

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A demand-based optimization approach to find market equilibria in oligopolies

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Oligopolistic competition occurs often in transportation as well as in other markets due to reasons such as barriers to entry, limited capacity of the infrastructure and external regulations. In transport oligopolies, suppliers are profit maximizers and ta ...

2019