[Paper] Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy

Source: arXiv - 2512.17899v1

Overview

The paper introduces Distributionally Robust Imitation Policy (DRIP), a layered control architecture that blends two previously developed techniques—Taylor Series Imitation Learning (TaSIL) and ℓ₁‑Distributionally Robust Adaptive Control (ℓ₁‑DRAC)—to deliver certifiable autonomous behavior. By tackling both policy‑error‑induced and disturbance‑induced distribution shifts, DRIP promises safer, more reliable imitation‑learning systems that can be formally verified.

Key Contributions

• Unified Layered Architecture (LCA): Combines TaSIL (robust to policy errors) and ℓ₁‑DRAC (robust to aleatoric/epistemic uncertainties) into a single pipeline with well‑defined input–output contracts.
• Distributionally Robust Imitation Policy (DRIP): Formal definition of a control policy that is provably robust to two major sources of distribution shift in imitation learning.
• Certificate‑by‑Design Guarantees: Provides mathematical certificates (e.g., bounded tracking error, safety margins) for the entire control stack, not just individual components.
• Modular Integration of Learning Modules: Shows how perception or high‑level planning modules (often black‑box neural nets) can be safely wrapped by the DRIP layers.
• Experimental Validation: Demonstrates DRIP on benchmark dynamical systems (e.g., inverted pendulum, quadrotor) showing reduced error accumulation and improved resilience to disturbances compared with vanilla IL or isolated TaSIL/ℓ₁‑DRAC.

Methodology

1. Problem Decomposition

   • Layer 1 (TaSIL): Uses a first‑order Taylor expansion of the expert policy to generate a feedback linearization term that compensates for errors in the learned policy. This layer mitigates the “compounding error” problem typical of imitation learning.
   • Layer 2 (ℓ₁‑DRAC): Implements an ℓ₁‑adaptive controller that estimates and cancels unknown dynamics and external disturbances in real time, providing robustness to model mismatches and stochastic perturbations.

2. Interface Design

   • Each layer publishes a contract (e.g., bounded input magnitude, required state‑space region) that the downstream layer must satisfy.
   • The overall controller is the cascade of the two layers, with the output of TaSIL feeding into ℓ₁‑DRAC, which then drives the plant.

3. Robustness Analysis

   • The authors formulate a distributionally robust optimization problem where the worst‑case distribution of disturbances is captured by an ambiguity set (e.g., Wasserstein ball).
   • Using Lyapunov arguments and ℓ₁‑adaptive theory, they prove that the closed‑loop system remains stable and satisfies safety constraints for any disturbance within the ambiguity set.

4. Implementation Details

   • Demonstrated on simulated platforms with real‑time computation (< 5 ms per control step).
   • Neural‑network policies are trained offline on expert trajectories, then wrapped by the DRIP layers at runtime.

Results & Findings

• Error Accumulation: DRIP reduces cumulative tracking error by up to 65 % compared with vanilla imitation learning.
• Safety Guarantees: Formal certificates confirm that state constraints (e.g., joint limits, altitude bounds) are never violated under the modeled disturbance set.
• Computation: The layered approach adds only ~2 ms overhead per control cycle, making it viable for embedded real‑time systems.

Practical Implications

• Safer Autonomous Vehicles: DRIP can wrap perception‑driven planners (e.g., lane‑keeping nets) to guarantee that the vehicle respects safety envelopes even when sensor noise or model errors spike.
• Robotics & Drones: Developers can deploy learned manipulation policies on manipulators or UAVs without fearing catastrophic drift when the robot encounters unmodeled payloads or wind gusts.
• Rapid Prototyping: The modular contracts let teams mix‑and‑match learning components (vision, language) with proven adaptive controllers, shortening the verification cycle.
• Regulatory Compliance: Formal certificates generated by DRIP align with emerging standards for “certifiable AI” in safety‑critical domains, easing certification processes.

Limitations & Future Work

• Assumption of Linearizable Dynamics: TaSIL relies on a first‑order Taylor expansion; highly nonlinear or discontinuous dynamics may degrade performance.
• Ambiguity Set Choice: The robustness guarantees hinge on the selected distributional ambiguity set (e.g., Wasserstein radius). Over‑conservative choices can lead to unnecessarily sluggish control.
• Scalability to High‑Dimensional Systems: While the paper shows success on low‑to‑moderate dimensional platforms, extending DRIP to very high‑dimensional state spaces (e.g., humanoid robots) may require additional dimensionality‑reduction techniques.
• Real‑World Validation: Experiments are confined to simulation; future work should include hardware‑in‑the‑loop tests and field trials under varying environmental conditions.

Bottom line: DRIP offers a pragmatic pathway for developers to embed learning‑based modules into safety‑critical control loops while retaining formal performance guarantees—a step forward toward truly certifiable autonomous systems.

Authors

• Aditya Gahlawat
• Ahmed Aboudonia
• Sandeep Banik
• Naira Hovakimyan
• Nikolai Matni
• Aaron D. Ames
• Gioele Zardini
• Alberto Speranzon

Paper Information

• arXiv ID: 2512.17899v1
• Categories: eess.SY, cs.LG
• Published: December 19, 2025
• PDF: Download PDF