RADIUM: Predicting and Repairing End-to-End Robot Failures using Gradient-Accelerated Sampling

TL;DR

We address safety verification for autonomous systems by jointly predicting failure modes and repairing end-to-end policies in a closed-loop simulation. The method, RADIUM, casts failure prediction and repair as tempered Bayesian inference over environmental parameters $\boldsymbol{\phi}$ and policy parameters $\boldsymbol{\theta}$, sampling from $p_{\text{failure}}(\boldsymbol{\phi};\theta) \propto p_{\phi,0}(\boldsymbol{\phi}) e^{-{[J^* - J(\theta,\boldsymbol{\phi})]}_+}$ and $p_{\text{repair}}(\theta; \boldsymbol{\phi}_1,\dots,\boldsymbol{\phi}_n) \propto p_{\theta,0}(\theta;\theta_0) e^{-{\sum_i [J(\theta,\boldsymbol{\phi}_i) - J^*]_+/n}}$, using gradient-based (e.g., MALA) or gradient-free samplers aided by differentiable simulation and rendering. Theoretical results establish convergence guarantees and characterize the joint distribution induced by the iterative sampling, while experiments across 12 benchmarks (including vision-in-the-loop tasks) show that gradient-based RADIUM yields lower failure rates and costs, with up to $5\times$ sim2real robustness improvements and diverse failure coverage beyond traditional adversarial methods. The work demonstrates that interleaving failure sampling with policy repair yields more robust, representative failure modes and repaired controllers, and that differentiable pipelines substantially boost sample efficiency where available. Overall, RADIUM advances practical safety verification for complex autonomous systems by combining diverse failure exploration with end-to-end policy improvement and demonstrated hardware transfer.

Abstract

Before autonomous systems can be deployed in safety-critical applications, we must be able to understand and verify the safety of these systems. For cases where the risk or cost of real-world testing is prohibitive, we propose a simulation-based framework for a) predicting ways in which an autonomous system is likely to fail and b) automatically adjusting the system's design and control policy to preemptively mitigate those failures. Existing tools for failure prediction struggle to search over high-dimensional environmental parameters, cannot efficiently handle end-to-end testing for systems with vision in the loop, and provide little guidance on how to mitigate failures once they are discovered. We approach this problem through the lens of approximate Bayesian inference and use differentiable simulation and rendering for efficient failure case prediction and repair. For cases where a differentiable simulator is not available, we provide a gradient-free version of our algorithm, and we include a theoretical and empirical evaluation of the trade-offs between gradient-based and gradient-free methods. We apply our approach on a range of robotics and control problems, including optimizing search patterns for robot swarms, UAV formation control, and robust network control. Compared to optimization-based falsification methods, our method predicts a more diverse, representative set of failure modes, and we find that our use of differentiable simulation yields solutions that have up to 10x lower cost and requires up to 2x fewer iterations to converge relative to gradient-free techniques. In hardware experiments, we find that repairing control policies using our method leads to a 5x robustness improvement. Accompanying code and video can be found at https://mit-realm.github.io/radium/

Figures (9)

• Figure 1: An overview of our approach for closed-loop rare-event prediction, which efficiently predicts and repairs failures in autonomous systems. Our framework alternates between failure prediction and repair sub-solvers, which use a simulated environment to efficiently sample from the distributions \ref{['eq:failure_logprob_basic']} and \ref{['eq:repair_logprob_basic']}. We use differentiable rendering and simulation to accelerate our method with end-to-end gradients, but we also propose a gradient-free implementation.
• Figure 2: Example images rendered using our basic differentiable rendering engine. Bottom-right shows a depth-only image; the rest are RGB images with directional lighting.
• Figure 3: The different environments used in our simulation studies, including 3 domains without visual feedback and 4 domains with vision in the loop.
• Figure 4: Comparison of our method (gradient-free and gradient-based variants $R_0$ and $R_1$, respectively) and baseline methods on benchmark problems without vision in the loop, showing failure rate, mean cost, and 99th percentile cost on a test set of 1,000 randomly sampled $\phi$. The dashed gray lines separate gradient-free and gradient-based methods.
• Figure 5: Comparison of our method (gradient-free and gradient-based variants $R_0$ and $R_1$, respectively) and baseline methods on benchmark problems with vision in the loop, showing failure rate, mean cost, and max cost on a test set of 1,000 randomly sampled $\phi$. The dashed gray lines separate gradient-free and gradient-based methods.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2