Related papers: Lagrangian Duality for Constrained Deep Learning

In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…

In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…

Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…

In this paper we study how Lagrange duality is connected to optimization problems whose objective function is the difference of two convex functions, briefly called DC problems. We present two Lagrange dual problems, each of them obtained…

A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information…

Deep Learning (DL) models proved themselves to perform extremely well on a wide variety of learning tasks, as they can learn useful patterns from large data sets. However, purely data-driven models might struggle when very difficult…

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…

In this paper we present a new Lagrange dual problem associated to a primal DC optimization problem under the additivity condition (AC). As usual for DC programming, even weak duality is not guaranteed for free and, due to this issue, we…

Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The…

We clarify the role of approximate S-duality in effective supergravity theories that are the low energy limits of string theories, and show how this partial symmetry may be used to constrain effective lagrangians for gaugino condensation.

Deep energy-based models are powerful, but pose challenges for learning and inference (Belanger and McCallum, 2016). Tu and Gimpel (2018) developed an efficient framework for energy-based models by training "inference networks" to…

We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and…

We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…

Detecting, predicting, and alleviating traffic congestion are targeted at improving the level of service of the transportation network. With increasing access to larger datasets of higher resolution, the relevance of deep learning for such…

Given the ubiquity of multi-task in practical systems, Multi-Task Learning (MTL) has found widespread application across diverse domains. In real-world scenarios, these tasks often have different priorities. For instance, In web search,…

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…