Related papers: Techniques for Gradient Based Bilevel Optimization…

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that…

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…

In this work we propose an improvement of the $x$-space algorithm developed for solving a class of min--max bilevel optimization problems (Tang Y., Richard J.P.P., Smith J.C. (2016), A class of algorithms for mixed-integer bilevel min--max…

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…

In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…

We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

Bi-level optimization has achieved considerable success in contemporary machine learning applications, especially for given proper hyperparameters. However, due to the two-level optimization structure, commonly, researchers focus on two…

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

In this work, we present a method for minimizing the time required for a redundant dual-arm robot to follow a desired relative Cartesian path at constant path speed by optimizing its joint trajectories, subject to position, velocity, and…

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…