Related papers: A Tutorial on Dual Decomposition and Lagrangian Re…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…

Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time…

We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…

With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing…

Morphological declension, which aims to inflect nouns to indicate number, case and gender, is an important task in natural language processing (NLP). This research proposal seeks to address the degree to which Recurrent Neural Networks…

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…

Compositional, structured models are appealing because they explicitly decompose problems and provide interpretable intermediate outputs that give confidence that the model is not simply latching onto data artifacts. Learning these models…

We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…

Many state-of-the-art neural models for NLP are heavily parameterized and thus memory inefficient. This paper proposes a series of lightweight and memory efficient neural architectures for a potpourri of natural language processing (NLP)…

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…

A critical concern in data-driven decision making is to build models whose outcomes do not discriminate against some demographic groups, including gender, ethnicity, or age. To ensure non-discrimination in learning tasks, knowledge of the…

Abstraction is a core tenet of human cognition and communication. When composing natural language instructions, humans naturally evoke abstraction to convey complex procedures in an efficient and concise way. Yet, interpreting and grounding…

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…

Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

Pre-trained language models have been successful in natural language generation (NLG) tasks. While various decoding methods have been employed, they often produce suboptimal results. We first present an empirical analysis of three NLG…