aiqbench analysis
This paper introduces MADR, a novel framework combining Model Predictive Control with adversarial deep learning to solve high-dimensional zero-sum differential games efficiently. By integrating regular supervision into physics-informed methods, it overcomes convergence issues in Hamilton-Jacobi reachability while generating robust safe policies for robotic agents. The approach demonstrates significant performance gains over baselines in both simulation and real-world hardware deployments.
MADR: MPC-guided Adversarial DeepReach
arXiv:2510.18845v2 Announce Type: replace Abstract: Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensionality. Physics-informed deep learning is able to overcome this infeasibility, but itself suffers from slow and inaccurate convergence, primarily due to weak PDE gradients and the complexity of self-supervised learning. A few works, recently, have demonstrated that enriching the self-supervision process with regular supervision (based on the nature of the optimal control problem), greatly accelerates convergence and solution quality, however, these have been limited to single player problems and simple games. In this work, we introduce MADR: MPC-guided Adversarial DeepReach, a general framework to robustly approximate the two-player, zero-sum differential game value function. In doing so, MADR yields the corresponding optimal strategies for both players in zero-sum games as well as safe policies for worst-case robustness. We test MADR on a multitude of high-dimensional simulated and real robotic agents with varying dynamics and games, finding that our approach significantly out-performs state-of-the-art baselines in simulation and produces impressive results in hardware.
Abstract:Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensionality. Physics-informed deep learning is able to overcome this infeasibility, but itself suffers from slow and inaccurate convergence, primarily due to weak PDE gradients and the complexity of self-supervised learning. A few works, recently, have demonstrated that enriching the self-supervision process with regular supervision (based on the nature of the optimal control problem), greatly accelerates convergence and solution quality, however, these have been limited to single player problems and simple games. In this work, we introduce MADR: MPC-guided Adversarial DeepReach, a general framework to robustly approximate the two-player, zero-sum differential game value function. In doing so, MADR yields the corresponding optimal strategies for both players in zero-sum games as well as safe policies for worst-case robustness. We test MADR on a multitude of high-dimensional simulated and real robotic agents with varying dynamics and games, finding that our approach significantly out-performs state-of-the-art baselines in simulation and produces impressive results in hardware.
Robotics (cs.RO); Systems and Control (eess.SY)
arXiv:2510.18845 [cs.RO]
(or arXiv:2510.18845v2 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2510.18845 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 271 words
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