Multi-Resolution Online Deterministic Annealing: A Hierarchical and Progressive Learning Architecture

• URL: http://arxiv.org/abs/2212.08189v3
• Date: Tue, 21 Mar 2023 04:13:48 GMT
• Title: Multi-Resolution Online Deterministic Annealing: A Hierarchical and Progressive Learning Architecture
• Authors: Christos Mavridis and John Baras
• Abstract summary: We introduce a general-purpose hierarchical learning architecture that is based on the progressive partitioning of a possibly multi-resolution data space. We show that the solution of each optimization problem can be estimated online using gradient-free approximation updates. Asymptotic convergence analysis and experimental results are provided for supervised and unsupervised learning problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we introduce a general-purpose hierarchical learning architecture that is based on the progressive partitioning of a possibly multi-resolution data space. The optimal partition is gradually approximated by solving a sequence of optimization sub-problems that yield a sequence of partitions with increasing number of subsets. We show that the solution of each optimization problem can be estimated online using gradient-free stochastic approximation updates. As a consequence, a function approximation problem can be defined within each subset of the partition and solved using the theory of two-timescale stochastic approximation algorithms. This simulates an annealing process and defines a robust and interpretable heuristic method to gradually increase the complexity of the learning architecture in a task-agnostic manner, giving emphasis to regions of the data space that are considered more important according to a predefined criterion. Finally, by imposing a tree structure in the progression of the partitions, we provide a means to incorporate potential multi-resolution structure of the data space into this approach, significantly reducing its complexity, while introducing hierarchical variable-rate feature extraction properties similar to certain classes of deep learning architectures. Asymptotic convergence analysis and experimental results are provided for supervised and unsupervised learning problems.

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