Related papers: Lagrangian Duality for Constrained Deep Learning

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient…

The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields IDFs simultaneously. We pose this as an optimization problem with constraints…

In his monograph \emph{Conjugate Duality and Optimization}, Rockafellar puts forward a ``perturbation + duality'' method to obtain a dual problem for an original minimization problem. First, one embeds the minimization problem into a family…

Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not…

In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…

Deep learning neural networks have emerged as one of the most powerful classification tools for vision related applications. However, the computational and energy requirements associated with such deep nets can be quite high, and hence…

This paper discusses a new approach to the fundamental problem of learning optimal Q-functions. In this approach, optimal Q-functions are formulated as saddle points of a nonlinear Lagrangian function derived from the classic Bellman…

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…

We review basic concepts of convex duality, focusing on the very general and supremely useful Fenchel-Rockafellar duality. We summarize how this duality may be applied to a variety of reinforcement learning (RL) settings, including policy…

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is…

In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…

Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of…

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…

In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show the finite support (Haar) dual is equivalent to…

Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint…