Dynamic Bilevel Learning with Inexact Line Search

In various domains within imaging and data science, particularly when addressing tasks modeled utilizing the variational regularization approach, manually configuring regularization parameters presents a formidable challenge. The difficulty intensifies when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning is employed to learn suitable hyperparameters. However, due to the use of numerical solvers, the exact gradient with respect to the hyperparameters is unattainable, necessitating the use of methods relying on approximate gradients. State-of-the-art inexact methods a priori select a decreasing summable sequence of the required accuracy and only assure convergence given a sufficiently small fixed step size. Despite this, challenges persist in determining the Lipschitz constant of the hypergradient and identifying an appropriate fixed step size. Conversely, computing exact function values is not feasible, impeding the use of line search. In this work, we introduce a provably convergent inexact backtracking line search involving inexact function evaluations and hypergradients. We show convergence to a stationary point of the loss with respect to hyperparameters. Additionally, we propose an algorithm to determine the required accuracy dynamically. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation in variational regularization problems, alongside its robustness in terms of the initial accuracy and step size choices

Online Distributed Learning with Quantized Finite-Time Coordination

In this paper we consider online distributed learning problems. Online distributed learning refers to the process of training learning models on distributed data sources. In our setting a set of agents need to cooperatively train a learning model from streaming data. Differently from federated learning, the proposed approach does not rely on a central server but only on peer-to-peer communications among the agents. This approach is often used in scenarios where data cannot be moved to a centralized location due to privacy, security, or cost reasons. In order to overcome the absence of a central server, we propose a distributed algorithm that relies on a quantized, finite-time coordination protocol to aggregate the locally trained models. Furthermore, our algorithm allows for the use of stochastic gradients during local training. Stochastic gradients are computed using a randomly sampled subset of the local training data, which makes the proposed algorithm more efficient and scalable than traditional gradient descent. In our paper, we analyze the performance of the proposed algorithm in terms of the mean distance from the online solution. Finally, we present numerical results for a logistic regression task.Comment: To be presented at IEEE CDC'2

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Bethe Projections for Non-Local Inference

Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programming, collective graphical models, and forms of semi-supervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful non-local statistics of the latent variables, while maintaining tractable and provably fast inference using non-Euclidean projected gradient descent with a distance-generating function given by the Bethe entropy. We demonstrate the performance and flexibility of our method by (1) extracting structured citations from research papers by learning soft global constraints, (2) achieving state-of-the-art results on a widely-used handwriting recognition task using a novel learned non-convex inference procedure, and (3) providing a fast and highly scalable algorithm for the challenging problem of inference in a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201