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Robustness of Agentic AI Systems via Adversarially-Aligned Jacobian Regularization

Furkan Mumcu, Yasin Yilmaz

TL;DR

Adversarially-Aligned Jacobian Regularization (AAJR) is introduced, a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions and yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation.

Abstract

As Large Language Models (LLMs) transition into autonomous multi-agent ecosystems, robust minimax training becomes essential yet remains prone to instability when highly non-linear policies induce extreme local curvature in the inner maximization. Standard remedies that enforce global Jacobian bounds are overly conservative, suppressing sensitivity in all directions and inducing a large Price of Robustness. We introduce Adversarially-Aligned Jacobian Regularization (AAJR), a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions. We prove that AAJR yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation. Furthermore, we derive step-size conditions under which AAJR controls effective smoothness along optimization trajectories and ensures inner-loop stability. These results provide a structural theory for agentic robustness that decouples minimax stability from global expressivity restrictions.

Robustness of Agentic AI Systems via Adversarially-Aligned Jacobian Regularization

TL;DR

Adversarially-Aligned Jacobian Regularization (AAJR) is introduced, a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions and yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation.

Abstract

As Large Language Models (LLMs) transition into autonomous multi-agent ecosystems, robust minimax training becomes essential yet remains prone to instability when highly non-linear policies induce extreme local curvature in the inner maximization. Standard remedies that enforce global Jacobian bounds are overly conservative, suppressing sensitivity in all directions and inducing a large Price of Robustness. We introduce Adversarially-Aligned Jacobian Regularization (AAJR), a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions. We prove that AAJR yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation. Furthermore, we derive step-size conditions under which AAJR controls effective smoothness along optimization trajectories and ensures inner-loop stability. These results provide a structural theory for agentic robustness that decouples minimax stability from global expressivity restrictions.
Paper Structure (23 sections, 5 theorems, 47 equations)

This paper contains 23 sections, 5 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation and Multi-Agent Objective
  4. Minimax Optimization and GDA Dynamics
  5. Lipschitz Continuity and the Policy Jacobian
  6. Problem Formulation
  7. Stability Requirement and Global Sensitivity Control
  8. Globally Constrained Policy Class
  9. Price of Robustness
  10. Core bottleneck.
  11. Standing Assumptions
  12. Directional Jacobian Constraints for Structural Agentic Robustness
  13. Adversarial Ascent Trajectories and Directional Sensitivity
  14. Adaptive Hypothesis Class and Price-of-Robustness Implications
  15. A Practical Surrogate: Adversarially-Aligned Jacobian Regularization
  16. ...and 8 more sections

Key Result

Proposition 1

If $\pi\in \mathcal{F}_\gamma$ and $\gamma \le \gamma_{\mathrm{adv}}$, then $\pi \in \mathcal{F}_{\mathrm{ad}}(\gamma_{\mathrm{adv}})$.

Theorems & Definitions (9)

  • Proposition 1: Global constraints imply directional constraints
  • Theorem 1: Class inclusion and strict expansion
  • proof
  • Corollary 1: Price-of-robustness ordering
  • proof
  • Theorem 2: Trajectory-wise effective directional smoothness
  • proof
  • Theorem 3: Stability of PGA under Directional Jacobian Control
  • proof