Game-Theoretic Defenses for Adversarially Robust Conformal Prediction

Adversarial attacks pose major challenges to the reliability of deep learning models in safety-critical domains such as medical imaging and autonomous driving. In such high-stakes applications, providing reliable uncertainty quantification alongside adversarial robustness becomes crucial for safe deployment. Although conformal prediction can provide certain guarantees for model performance under such conditions, unknown attacks may violate the exchangeability assumption, resulting in the loss of coverage guarantees or excessively large predictive uncertainty. To address this, we propose a synergistic framework that integrates conformal prediction with game-theoretic defense strategies by modeling the adversarial interaction as a discrete, zero-sum game between attacker and defender. Our framework yields a Nash Equilibrium defense strategy, which we prove maintains valid coverage while minimizing the worst-case prediction set size against an optimal adversary operating within the defined attack space. Experimental results on CIFAR-10, CIFAR-100, and ImageNet further demonstrate that, under Nash equilibrium, defense models within our framework achieve valid coverage and minimal prediction set size. By bridging adversarial robustness and uncertainty quantification from a game-theoretic perspective, this work provides a verifiable defense paradigm for deploying safety-critical deep learning systems, particularly when adversarial distributions are unknown or dynamically evolving but contained within a known attack space. The Python code is available at https://github.com/bjbbbb/Game-Theoretic-CP.