相关论文: A novel approach for bilevel programs based on Wol…

We consider infinite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can…

Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes. However, these algorithms generally do not optimize a scalar objective function. In this paper, we draw connections between DP and (constrained)…

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…

This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Bilevel optimization has arisen as a powerful tool for solving a variety of machine learning problems. Two current popular bilevel optimizers AID-BiO and ITD-BiO naturally involve solving one or two sub-problems, and consequently, whether…

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

We investigate the dual of a Multistage Stochastic Linear Program (MSLP) to study two questions for this class of problems. The first of these questions is the study of the optimal value of the problem as a function of the involved…

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering…

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…

In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…

Bilevel optimization (BLO) offers a principled framework for hierarchical decision-making and has been widely applied in machine learning tasks such as hyperparameter optimization and meta-learning. While existing BLO methods are mostly…

We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block…

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple…

We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…