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Adversarially Robust Multitask Adaptive Control

Kasra Fallah, Leonardo F. Toso, James Anderson

TL;DR

The paper tackles adversarially robust multitask adaptive LQR control for heterogeneous, potentially compromised systems. It introduces a clustered multitask learning pipeline that clusters systems, performs robust multitask system identification within clusters, and uses resilient aggregation to suppress Byzantine updates. The authors derive non-asymptotic error and regret bounds showing that collaboration reduces regret roughly as rac{dT}{m_j}^{1/2} and that this benefit persists under bounded adversarial fractions, with additional terms capturing clustering misclassification and intra-cluster heterogeneity. Numerical experiments on simulated multi-robot dynamics validate the approach, illustrating improved performance over single-task CE control and robustness to adversarial behavior, with insights into the interaction between clustering accuracy, heterogeneity, and resilience.

Abstract

We study adversarially robust multitask adaptive linear quadratic control; a setting where multiple systems collaboratively learn control policies under model uncertainty and adversarial corruption. We propose a clustered multitask approach that integrates clustering and system identification with resilient aggregation to mitigate corrupted model updates. Our analysis characterizes how clustering accuracy, intra-cluster heterogeneity, and adversarial behavior affect the expected regret of certainty-equivalent (CE) control across LQR tasks. We establish non-asymptotic bounds demonstrating that the regret decreases inversely with the number of honest systems per cluster and that this reduction is preserved under a bounded fraction of adversarial systems within each cluster.

Adversarially Robust Multitask Adaptive Control

TL;DR

The paper tackles adversarially robust multitask adaptive LQR control for heterogeneous, potentially compromised systems. It introduces a clustered multitask learning pipeline that clusters systems, performs robust multitask system identification within clusters, and uses resilient aggregation to suppress Byzantine updates. The authors derive non-asymptotic error and regret bounds showing that collaboration reduces regret roughly as rac{dT}{m_j}^{1/2} and that this benefit persists under bounded adversarial fractions, with additional terms capturing clustering misclassification and intra-cluster heterogeneity. Numerical experiments on simulated multi-robot dynamics validate the approach, illustrating improved performance over single-task CE control and robustness to adversarial behavior, with insights into the interaction between clustering accuracy, heterogeneity, and resilience.

Abstract

We study adversarially robust multitask adaptive linear quadratic control; a setting where multiple systems collaboratively learn control policies under model uncertainty and adversarial corruption. We propose a clustered multitask approach that integrates clustering and system identification with resilient aggregation to mitigate corrupted model updates. Our analysis characterizes how clustering accuracy, intra-cluster heterogeneity, and adversarial behavior affect the expected regret of certainty-equivalent (CE) control across LQR tasks. We establish non-asymptotic bounds demonstrating that the regret decreases inversely with the number of honest systems per cluster and that this reduction is preserved under a bounded fraction of adversarial systems within each cluster.

Paper Structure

This paper contains 28 sections, 20 theorems, 124 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Notation
  5. Problem Setup
  6. Certainty-Equivalent Linear Quadratic Control
  7. Multitask Adaptive Control
  8. Adversarial Systems
  9. Error Bounds for Multitask System Identification
  10. Regret Analysis
  11. Proof Idea
  12. Numerical Validation
  13. Future Work
  14. Acknowledgments
  15. Appendix
  16. ...and 13 more sections

Key Result

Theorem 1.1

Consider the multitask adaptive linear quadratic control pipeline illustrated in Figure fig:multitask_control_pipeline. For an appropriate choice of exploration and a sufficiently large amount of data per system, let $T$ denote the time horizon, $m_j$ the number of honest systems in cluster $\mathca where $ \lesssim \exp(\textcolor{Green}{-\#~data samples per system}).$

Figures (2)

  • Figure 1: Workflow for adversarially robust multitask adaptive control$^\dagger$.
  • Figure 2: Illustration of main results. Top row--(left) homogeneous clusters; (middle) intra-cluster heterogeneity; (right) misclassification rate. Bottom row--(left) adversarial systems; (middle) robust aggregation comparison; (right) comparison with multitask representation learning.

Theorems & Definitions (31)

  • Theorem 1.1: Informal
  • Definition 2.1: $(f, \lambda)$-Resilient aggregation - Adapted from farhadkhani2022byzantine
  • Remark 2.1
  • Remark 2.2
  • Lemma 3.1: Intra-cluster homogeneity
  • Proposition 3.1: Intra-cluster heterogeneity
  • Lemma 3.2: Adversarial systems
  • Theorem 4.1: Intra-cluster homogeneity
  • Corollary 4.1: Intra-cluster heterogeneity
  • Theorem 4.2: Adversarial systems
  • ...and 21 more