In uncertainty quantification, evaluating sensitivity measures under specific conditions (i.e., conditional Sobol' indices) is essential for systems with parameterized responses, such as spatial fields or varying operating conditions. Traditional approaches often rely on point-wise modeling, which is computationally expensive and may lack consistency across the parameter space. This paper demonstrates that for a pre-trained global Polynomial Chaos Expansion (PCE) model, the analytical conditional Sobol' indices are inherently embedded within its basis functions. By leveraging the tensor-product property of PCE bases, we reformulate the global expansion into a set of analytical coefficient fields that depend on the conditioning variables. Based on the preservation of orthogonality under conditional probability measures, we derive closed-form expressions for conditional variances and Sobol' indices. This framework bypasses the need for repetitive modeling or additional sampling, transforming conditional sensitivity analysis into a purely algebraic post-processing step. Numerical benchmarks indicate that the proposed method ensures physical coherence and offers superior numerical robustness and computational efficiency compared to conventional point-wise approaches.

Typically, forecasts are designed without knowledge of a downstream controller's task objective, and thus simply optimize formean prediction error. However, such task-agnostic representations are often too large to stream over a communication network and do not emphasize salient temporal features for cooperativecontrol.

We precisely characterize the expressivity of computable Recurrent Graph Neural Networks (recurrent GNNs). We prove that recurrent GNNs with finite-precision parameters, sum aggregation, and ReLU activation, can compute any graph algorithm that respects the natural message-passing invariance induced by the Color Refinement (or Weisfeiler-Leman) algorithm. While it is well known that the expressive power of GNNs is limited by this invariance [Morris et al., AAAI 2019; Xu et al., ICLR 2019], we establish that recurrent GNNs can actually match this limit. This is in contrast to non-recurrent GNNs, which have the power of Weisfeiler-Leman only in a very weak, "non-uniform", sense where each graph size requires a different GNN to compute with. Our construction introduces only a polynomial overhead in both time and space. Furthermore, we show that by incorporating random initialization, for connected graphs recurrent GNNs can express all graph algorithms. In particular, any polynomial-time graph algorithm can be emulated on connected graphs in polynomial time by a recurrent GNN with random initialization.

Uncertainty-aware prediction is essential for safe motion planning, especially when using learned models to forecast the behavior of surrounding agents. Conformal prediction is a statistical tool often used to produce uncertainty-aware prediction regions for machine learning models. Most existing frameworks utilizing conformal prediction-based uncertainty predictions assume that the surrounding agents are non-interactive. This is because in closed-loop, as uncertainty-aware agents change their behavior to account for prediction uncertainty, the surrounding agents respond to this change, leading to a distribution shift which we call endogenous distribution shift. To address this challenge, we introduce an iterative conformal prediction framework that systematically adapts the uncertainty-aware ego-agent controller to the endogenous distribution shift. The proposed method provides probabilistic safety guarantees while adapting to the evolving behavior of reactive, non-ego agents. We establish a model for the endogenous distribution shift and provide the conditions for the iterative conformal prediction pipeline to converge under such a distribution shift. We validate our framework in simulation for 2- and 3- agent interaction scenarios, demonstrating collision avoidance without resulting in overly conservative behavior and an overall improvement in success rates of up to 9.6% compared to other conformal prediction-based baselines.

This paper demonstrates how reinforcement learning can explain two puzzling empirical patterns in household consumption behavior during economic downturns. I develop a model where agents use Q-learning with neural network approximation to make consumption-savings decisions under income uncertainty, departing from standard rational expectations assumptions. The model replicates two key findings from recent literature: (1) unemployed households with previously low liquid assets exhibit substantially higher marginal propensities to consume (MPCs) out of stimulus transfers compared to high-asset households (0.50 vs 0.34), even when neither group faces borrowing constraints, consistent with Ganong et al. (2024); and (2) households with more past unemployment experiences maintain persistently lower consumption levels after controlling for current economic conditions, a "scarring" effect documented by Malmendier and Shen (2024). Unlike existing explanations based on belief updating about income risk or ex-ante heterogeneity, the reinforcement learning mechanism generates both higher MPCs and lower consumption levels simultaneously through value function approximation errors that evolve with experience. Simulation results closely match the empirical estimates, suggesting that adaptive learning through reinforcement learning provides a unifying framework for understanding how past experiences shape current consumption behavior beyond what current economic conditions would predict.

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