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Efficient Implementation of LinearUCB through Algorithmic Improvements and Vector Computing Acceleration for Embedded Learning Systems

Marco Angioli, Marcello Barbirotta, Abdallah Cheikh, Antonio Mastrandrea, Francesco Menichelli, Mauro Olivieri

TL;DR

The paper tackles embedding LinearUCB contextual bandits on energy-limited edge devices by pairing algorithmic updates (Sherman-Morrison and Woodbury) with vector-accelerated hardware. By avoiding full matrix inversions and exploiting incremental inverse updates, the Disjoint and Hybrid variants achieve substantial reductions in execution time and memory use while maintaining numerical stability. Empirical results across multiple embedded platforms demonstrate up to tens of times speedups and significant energy savings, with vector acceleration providing additional gains that scale with matrix size. The combined approach broadens the practical applicability of online, edge-based learning in real-time, low-power IoT environments.

Abstract

As the Internet of Things expands, embedding Artificial Intelligence algorithms in resource-constrained devices has become increasingly important to enable real-time, autonomous decision-making without relying on centralized cloud servers. However, implementing and executing complex algorithms in embedded devices poses significant challenges due to limited computational power, memory, and energy resources. This paper presents algorithmic and hardware techniques to efficiently implement two LinearUCB Contextual Bandits algorithms on resource-constrained embedded devices. Algorithmic modifications based on the Sherman-Morrison-Woodbury formula streamline model complexity, while vector acceleration is harnessed to speed up matrix operations. We analyze the impact of each optimization individually and then combine them in a two-pronged strategy. The results show notable improvements in execution time and energy consumption, demonstrating the effectiveness of combining algorithmic and hardware optimizations to enhance learning models for edge computing environments with low-power and real-time requirements.

Efficient Implementation of LinearUCB through Algorithmic Improvements and Vector Computing Acceleration for Embedded Learning Systems

TL;DR

The paper tackles embedding LinearUCB contextual bandits on energy-limited edge devices by pairing algorithmic updates (Sherman-Morrison and Woodbury) with vector-accelerated hardware. By avoiding full matrix inversions and exploiting incremental inverse updates, the Disjoint and Hybrid variants achieve substantial reductions in execution time and memory use while maintaining numerical stability. Empirical results across multiple embedded platforms demonstrate up to tens of times speedups and significant energy savings, with vector acceleration providing additional gains that scale with matrix size. The combined approach broadens the practical applicability of online, edge-based learning in real-time, low-power IoT environments.

Abstract

As the Internet of Things expands, embedding Artificial Intelligence algorithms in resource-constrained devices has become increasingly important to enable real-time, autonomous decision-making without relying on centralized cloud servers. However, implementing and executing complex algorithms in embedded devices poses significant challenges due to limited computational power, memory, and energy resources. This paper presents algorithmic and hardware techniques to efficiently implement two LinearUCB Contextual Bandits algorithms on resource-constrained embedded devices. Algorithmic modifications based on the Sherman-Morrison-Woodbury formula streamline model complexity, while vector acceleration is harnessed to speed up matrix operations. We analyze the impact of each optimization individually and then combine them in a two-pronged strategy. The results show notable improvements in execution time and energy consumption, demonstrating the effectiveness of combining algorithmic and hardware optimizations to enhance learning models for edge computing environments with low-power and real-time requirements.
Paper Structure (22 sections, 14 equations, 14 figures, 3 tables, 2 algorithms)

This paper contains 22 sections, 14 equations, 14 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Works
  3. Background
  4. Related Works
  5. Algorithmic Optimizations
  6. Optimization of the Disjoint LinearUCB through the Sherman-Morrison Formula
  7. Optimization of the Hybrid LinearUCB through the Woodbury's Formula
  8. Stability and Round-off Errors
  9. Stability of the Covariance Matrices
  10. Assessing the Accumulation of Round-Off Errors
  11. Proposed Solution to Mitigate Round-Off Errors
  12. Vector Computing Acceleration
  13. Reference Embedded Vector Computing Platform
  14. Mapping LinearUCB algorithms on the vector accelerator
  15. Results on full algorithm execution
  16. ...and 7 more sections

Figures (14)

  • Figure 1: Computational complexity trends for the standard Disjoint Algorithm and the proposed optimized version.
  • Figure 2: Stack Memory Usage for the standard Disjoint Algorithm and the proposed optimized version.
  • Figure 3: Computational complexity trends for the standard Hybrid Algorithm and the proposed optimized version.
  • Figure 4: Stack Memory Usage for the standard Hybrid Algorithm and the proposed optimized version.
  • Figure 5: Error growth in the Disjoint Linear UCB algorithm, measured by the Frobenius norm of the difference between $\mathbf{A}_{a_t}^{-1}$ (computed incrementally) and the same matrix obtained via full inversion.
  • ...and 9 more figures