Mathematical framework for robust autonomous driving via stochastic graph optimization and CVaR policies

Autonomous driving under stochastic sensor failures poses a mathematically challenging problem of learning with partially observed, dynamically structured data. Existing approaches often lack rigorous mechanisms to guarantee robustness, particularly in the presence of missing features and uncertain communication reliability. To overcome these limitations, we propose a mathematically grounded unified optimization framework that integrates V2X-based cooperative sensing, graph-regularized feature imputation, and risk-aware decision generation. The pipeline is optimized via a hybrid strategy combining stochastic gradient descent, variance reduction, and the Alternating Direction Method of Multipliers (ADMM)-based consensus, ensuring stable convergence for both convex and non-convex components. Empirical validation shows that our framework reduces perception error by 18.7 %, improves decision consistency by 15.3 %, and accelerates convergence by 1.8 × compared with state-of-the-art baselines under stochastic sensor failures across diverse driving environments. Beyond these empirical gains, the explicit incorporation of reliability-weighted graph embeddings and Conditional Value-at-Risk (CVaR)-based optimization provides theoretical robustness guarantees against rare but high-risk events. Unlike risk-neutral formulations, CVaR minimizes the expected tail loss, making it particularly suitable for safety-critical autonomous driving systems where uncertainty and risk interact. Overall, the proposed method delivers both mathematical rigor and practical deployability, offering a concise and extensible blueprint for robust and reliable optimization in distributed autonomous driving systems.