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In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…
Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…
We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
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.…
This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…
Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…
Temporal-Difference (TD) learning with nonlinear smooth function approximation for policy evaluation has achieved great success in modern reinforcement learning. It is shown that such a problem can be reformulated as a stochastic…
We consider the problem of minimizing the sum of a Lipschitz differentiable convex function $f$ and a proper closed convex function $h$ that admits efficient linear minimization oracles, subject to multiple smooth convex inequality…
Gradient descent ascent (GDA), the simplest single-loop algorithm for nonconvex minimax optimization, is widely used in practical applications such as generative adversarial networks (GANs) and adversarial training. Albeit its desirable…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…
We provide a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a recent small-gain theorem of Angeli and Sontag for monotone systems with…
In this paper, we propose a single-loop stochastic gradient algorithm for solving stochastic nonconvex-concave minimax optimization with nonlinear convex coupled constraints (MCC). The proposed method, SPACO (Stochastic Penalty-based…
In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…
While variance reduction methods have shown great success in solving large scale optimization problems, many of them suffer from accumulated errors and, therefore, should periodically require the full gradient computation. In this paper, we…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale empirical risk minimization setting where the number of samples…