Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being \emph{reusable}: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the \emph{semantic basis}, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a \emph{rolling prediction monitor} that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.

Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable - forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs - a direct consequence of using all available data for shape optimization and calibration simultaneously.

UMBRELLA: Uncertainty-aware Multi-robot Reactive Coordination under Dynamic Temporal Logic Tasks

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Prediction

Autonomous systems operate in environments that may change over time. An example is the control of a self-driving vehicle among pedestrians and human-controlled vehicles whose behavior may change based on factors such as traffic density, road visibility, and social norms. Therefore, the environment encountered during deployment rarely mirrors the environment and data encountered during training -- a phenomenon known as distribution shift -- which can undermine the safety of autonomous systems. Conformal prediction (CP) has recently been used along with data from the training environment to provide prediction regions that capture the behavior of the environment with a desired probability. When embedded within a model predictive controller (MPC), one can provide probabilistic safety guarantees, but only when the deployment and training environments coincide. Once a distribution shift occurs, these guarantees collapse. We propose a planning framework that is robust under distribution shifts by: (i) assuming that the underlying data distribution of the environment is parameterized by a nuisance parameter, i.e., an observable, interpretable quantity such as traffic density, (ii) training a conditional diffusion model that captures distribution shifts as a function of the nuisance parameter, (iii) observing the nuisance parameter online and generating cheap, synthetic data from the diffusion model for the observed nuisance parameter, and (iv) designing an MPC that embeds CP regions constructed from such synthetic data. Importantly, we account for discrepancies between the underlying data distribution and the diffusion model by using robust CP. Thus, the plans computed using robust CP enjoy probabilistic safety guarantees, in contrast with plans obtained from a single, static set of training data. We empirically demonstrate safety under diverse distribution shifts in the ORCA simulator.

eCP: Informative uncertainty quantification via Equivariantized Conformal Prediction with pre-trained models

We study the effect of group symmetrization of pre-trained models on conformal prediction (CP), a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, CP uncertainty regions can grow significantly in long horizon missions, rendering the statistical guarantees uninformative. To that end, we propose infusing CP with geometric information via group-averaging of the pretrained predictor to distribute the non-conformity mass across the orbits. Each sample now is treated as a representative of an orbit, thus uncertainty can be mitigated by other samples entangled to it via the orbit inducing elements of the symmetry group. Our approach provably yields contracted non-conformity scores in increasing convex order, implying improved exponential-tail bounds and sharper conformal prediction sets in expectation, especially at high confidence levels. We then propose an experimental design to test these theoretical claims in pedestrian trajectory prediction.

Safe Planning in Interactive Environments via Iterative Policy Updates and Adversarially Robust Conformal Prediction

Safe planning of an autonomous agent in interactive environments -- such as the control of a self-driving vehicle among pedestrians and human-controlled vehicles -- poses a major challenge as the behavior of the environment is unknown and reactive to the behavior of the autonomous agent. This coupling gives rise to interaction-driven distribution shifts where the autonomous agent's control policy may change the environment's behavior, thereby invalidating safety guarantees in existing work. Indeed, recent works have used conformal prediction (CP) to generate distribution-free safety guarantees using observed data of the environment. However, CP's assumption on data exchangeability is violated in interactive settings due to a circular dependency where a control policy update changes the environment's behavior, and vice versa. To address this gap, we propose an iterative framework that robustly maintains safety guarantees across policy updates by quantifying the potential impact of a planned policy update on the environment's behavior. We realize this via adversarially robust CP where we perform a regular CP step in each episode using observed data under the current policy, but then transfer safety guarantees across policy updates by analytically adjusting the CP result to account for distribution shifts. This adjustment is performed based on a policy-to-trajectory sensitivity analysis, resulting in a safe, episodic open-loop planner. We further conduct a contraction analysis of the system providing conditions under which both the CP results and the policy updates are guaranteed to converge. We empirically demonstrate these safety and convergence guarantees on a two-dimensional car-pedestrian case study. To the best of our knowledge, these are the first results that provide valid safety guarantees in such interactive settings.

Split Conformal Prediction in the Function Space with Neural Operators

Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample guarantees in finite-dimensional spaces, it does not directly extend to function-valued outputs. Existing approaches (Gaussian processes, Bayesian neural networks, and quantile-based operators) require strong distributional assumptions or yield conservative coverage. This work extends split conformal prediction to function spaces following a two step method. We first establish finite-sample coverage guarantees in a finite-dimensional space using a discretization map in the output function space. Then these guarantees are lifted to the function-space by considering the asymptotic convergence as the discretization is refined. To characterize the effect of resolution, we decompose the conformal radius into discretization, calibration, and misspecification components. This decomposition motivates a regression-based correction to transfer calibration across resolutions. Additionally, we propose two diagnostic metrics (conformal ensemble score and internal agreement) to quantify forecast degradation in autoregressive settings. Empirical results show that our method maintains calibrated coverage with less variation under resolution shifts and achieves better coverage in super-resolution tasks.

Multi-Agent Path Finding Among Dynamic Uncontrollable Agents with Statistical Safety Guarantees

Existing multi-agent path finding (MAPF) solvers do not account for uncertain behavior of uncontrollable agents. We present a novel variant of Enhanced Conflict-Based Search (ECBS), for both one-shot and lifelong MAPF in dynamic environments with uncontrollable agents. Our method consists of (1) training a learned predictor for the movement of uncontrollable agents, (2) quantifying the prediction error using conformal prediction (CP), a tool for statistical uncertainty quantification, and (3) integrating these uncertainty intervals into our modified ECBS solver. Our method can account for uncertain agent behavior, comes with statistical guarantees on collision-free paths for one-shot missions, and scales to lifelong missions with a receding horizon sequence of one-shot instances. We run our algorithm, CP-Solver, across warehouse and game maps, with competitive throughput and reduced collisions.

Deep Equivariant Multi-Agent Control Barrier Functions

With multi-agent systems increasingly deployed autonomously at scale in complex environments, ensuring safety of the data-driven policies is critical. Control Barrier Functions have emerged as an effective tool for enforcing safety constraints, yet existing learning-based methods often lack in scalability, generalization and sampling efficiency as they overlook inherent geometric structures of the system. To address this gap, we introduce symmetries-infused distributed Control Barrier Functions, enforcing the satisfaction of intrinsic symmetries on learnable graph-based safety certificates. We theoretically motivate the need for equivariant parametrization of CBFs and policies, and propose a simple, yet efficient and adaptable methodology for constructing such equivariant group-modular networks via the compatible group actions. This approach encodes safety constraints in a distributed data-efficient manner, enabling zero-shot generalization to larger and denser swarms. Through extensive simulations on multi-robot navigation tasks, we demonstrate that our method outperforms state-of-the-art baselines in terms of safety, scalability, and task success rates, highlighting the importance of embedding symmetries in safe distributed neural policies.

PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis

This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical systems. However, identifying parametric physical models for complex CPS is challenging due to their complexity, uncertainty, and variability, often rendering them as black-box oracles. As an alternative, one can treat these complex systems as black-box models and use trajectory data sampled from the system (e.g., from high-fidelity simulators or the real system) along with machine learning techniques to learn models that approximate the underlying dynamics. However, these machine learning models can be inaccurate, highlighting the need for statistical tools to quantify errors. Recent advancements in the field include the incorporation of statistical uncertainty quantification tools such as conformal inference (CI) that can provide probabilistic reachable sets with provable guarantees. Recent work has even highlighted the ability of these tools to address the case where the distribution of trajectories sampled during training time are different from the distribution of trajectories encountered during deployment time. However, accounting for such distribution shifts typically results in more conservative guarantees. This is undesirable in practice and motivates us to present techniques that can reduce conservatism. Here, we propose a new approach that reduces conservatism and improves scalability by combining conformal inference with Principal Component Analysis (PCA). We show the effectiveness of our technique on various case studies, including a 12-dimensional quadcopter and a 27-dimensional hybrid system known as the powertrain.