Robust Belief-Space Games: Algorithms for Adversarial Control Under Uncertainty

Gordei Verbii

Keywords: robust control, belief space, dynamic games, Hamilton-Jacobi-Bellman-Isaacs, particle filtering, adversarial learning

TL;DR: The paper introduces Gaussian Game-iLQG and Particle Min-Max Game, two algorithms that solve robust control under uncertainty by treating it as a zero-sum dynamic game in belief space.

Abstract: This paper presents a comprehensive framework for robust control in belief space under adversarial disturbances, addressing the fundamental challenge of optimal decision-making when both state uncertainty and adversarial perturbations are present. We formulate the problem as a zero-sum dynamic game in the space of probability distributions (belief space) and derive computationally tractable algorithms through finite-dimensional approximations. Our approach includes two novel CPU-efficient methods: (1) Gaussian Game-iLQG, which reduces the infinite-dimensional Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation to finite-dimensional Riccati-type equations through Gaussian belief approximation, and (2) Particle Min-Max Game, which employs sample-based belief representation with alternating optimization. Extensive numerical experiments on 2D navigation and racing scenarios demonstrate that our methods achieve 15-20\% better worst-case performance compared to standard robust control approaches while maintaining computational efficiency suitable for real-time applications. The theoretical analysis provides convergence guarantees and robustness bounds, while empirical validation shows 92-95\% success rates in adversarial environments with computation times under 3 seconds on standard CPU hardware.

Submission Number: 12