Safety Evaluation of Motion Plans Using Trajectory Predictors as Forward Reachable Set Estimators

The advent of end-to-end autonomy stacks - often lacking interpretable intermediate modules - has placed an increased burden on ensuring that the final output, i.e., the motion plan, is safe in order to validate the safety of the entire stack. This requires a safety monitor that is both complete (able to detect all unsafe plans) and sound (does not flag safe plans). In this work, we propose a principled safety monitor that leverages modern multi-modal trajectory predictors to approximate forward reachable sets (FRS) of surrounding agents. By formulating a convex program, we efficiently extract these data-driven FRSs directly from the predicted state distributions, conditioned on scene context such as lane topology and agent history. To ensure completeness, we leverage conformal prediction to calibrate the FRS and guarantee coverage of ground-truth trajectories with high probability. To preserve soundness in out-of-distribution (OOD) scenarios or under predictor failure, we introduce a Bayesian filter that dynamically adjusts the FRS conservativeness based on the predictor's observed performance. We then assess the safety of the ego vehicle's motion plan by checking for intersections with these calibrated FRSs, ensuring the plan remains collision-free under plausible future behaviors of others. Extensive experiments on the nuScenes dataset show our approach significantly improves soundness while maintaining completeness, offering a practical and reliable safety monitor for learned autonomy stacks.

ASP-Assisted Symbolic Regression: Uncovering Hidden Physics in Fluid Mechanics

Unlike conventional Machine-Learning (ML) approaches, often criticized as "black boxes", Symbolic Regression (SR) stands out as a powerful tool for revealing interpretable mathematical relationships in complex physical systems, requiring no a priori assumptions about models' structures. Motivated by the recognition that, in fluid mechanics, an understanding of the underlying flow physics is as crucial as accurate prediction, this study applies SR to model a fundamental three-dimensional (3D) incompressible flow in a rectangular channel, focusing on the (axial) velocity and pressure fields under laminar conditions. By employing the PySR library, compact symbolic equations were derived directly from numerical simulation data, revealing key characteristics of the flow dynamics. These equations not only approximate the parabolic velocity profile and pressure drop observed in the studied fluid flow, but also perfectly coincide with analytical solutions from the literature. Furthermore, we propose an innovative approach that integrates SR with the knowledge-representation framework of Answer Set Programming (ASP), combining the generative power of SR with the declarative reasoning strengths of ASP. The proposed hybrid SR/ASP framework ensures that the SR-generated symbolic expressions are not only statistically accurate, but also physically plausible, adhering to domain-specific principles. Overall, the study highlights two key contributions: SR's ability to simplify complex flow behaviours into concise, interpretable equations, and the potential of knowledge-representation approaches to improve the reliability and alignment of data-driven SR models with domain principles. Insights from the examined 3D channel flow pave the way for integrating such hybrid approaches into efficient frameworks, [...] where explainable predictions and real-time data analysis are crucial.

Partially Observable Reference Policy Programming: Solving POMDPs Sans Numerical Optimisation

This paper proposes Partially Observable Reference Policy Programming, a novel anytime online approximate POMDP solver which samples meaningful future histories very deeply while simultaneously forcing a gradual policy update. We provide theoretical guarantees for the algorithm's underlying scheme which say that the performance loss is bounded by the average of the sampling approximation errors rather than the usual maximum, a crucial requirement given the sampling sparsity of online planning. Empirical evaluations on two large-scale problems with dynamically evolving environments -- including a helicopter emergency scenario in the Corsica region requiring approximately 150 planning steps -- corroborate the theoretical results and indicate that our solver considerably outperforms current online benchmarks.

SlimCaching: Edge Caching of Mixture-of-Experts for Distributed Inference

Mixture-of-Experts (MoE) models improve the scalability of large language models (LLMs) by activating only a small subset of relevant experts per input. However, the sheer number of expert networks in an MoE model introduces a significant storage burden for an edge device. To address this challenge, we consider a scenario where experts are dispersed within an edge network for distributed inference. Based on the popular Top-$K$ expert selection strategy, we formulate a latency minimization problem by optimizing expert caching on edge servers under storage constraints. When $K=1$, the problem reduces to a monotone submodular maximization problem with knapsack constraints, for which we design a greedy-based algorithm with a $(1 - 1/e)$-approximation guarantee. For the general case where $K\geq1$, expert co-activation within the same MoE layer introduces non-submodularity, causing greedy methods to be ineffective. To tackle this issue, we propose a successive greedy decomposition method to decompose the original problem into a series of subproblems, with each being solved by a dynamic programming approach. Furthermore, we design an accelerated algorithm based on the max-convolution technique to obtain the approximate solution with a provable guarantee in polynomial time. Simulation results on various MoE models demonstrate that our method significantly reduces inference latency compared to existing baselines.

Joint Matching and Pricing for Crowd-shipping with In-store Customers

This paper examines the use of in-store customers as delivery couriers in a centralized crowd-shipping system, targeting the growing need for efficient last-mile delivery in urban areas. We consider a brick-and-mortar retail setting where shoppers are offered compensation to deliver time-sensitive online orders. To manage this process, we propose a Markov Decision Process (MDP) model that captures key uncertainties, including the stochastic arrival of orders and crowd-shippers, and the probabilistic acceptance of delivery offers. Our solution approach integrates Neural Approximate Dynamic Programming (NeurADP) for adaptive order-to-shopper assignment with a Deep Double Q-Network (DDQN) for dynamic pricing. This joint optimization strategy enables multi-drop routing and accounts for offer acceptance uncertainty, aligning more closely with real-world operations. Experimental results demonstrate that the integrated NeurADP + DDQN policy achieves notable improvements in delivery cost efficiency, with up to 6.7\% savings over NeurADP with fixed pricing and approximately 18\% over myopic baselines. We also show that allowing flexible delivery delays and enabling multi-destination routing further reduces operational costs by 8\% and 17\%, respectively. These findings underscore the advantages of dynamic, forward-looking policies in crowd-shipping systems and offer practical guidance for urban logistics operators.

Neural Hamiltonian Operator

Stochastic control problems in high dimensions are notoriously difficult to solve due to the curse of dimensionality. An alternative to traditional dynamic programming is Pontryagin's Maximum Principle (PMP), which recasts the problem as a system of Forward-Backward Stochastic Differential Equations (FBSDEs). In this paper, we introduce a formal framework for solving such problems with deep learning by defining a \textbf{Neural Hamiltonian Operator (NHO)}. This operator parameterizes the coupled FBSDE dynamics via neural networks that represent the feedback control and an ansatz for the value function's spatial gradient. We show how the optimal NHO can be found by training the underlying networks to enforce the consistency conditions dictated by the PMP. By adopting this operator-theoretic view, we situate the deep FBSDE method within the rigorous language of statistical inference, framing it as a problem of learning an unknown operator from simulated data. This perspective allows us to prove the universal approximation capabilities of NHOs under general martingale drivers and provides a clear lens for analyzing the significant optimization challenges inherent to this class of models.

Dynamical System Optimization

We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize policy parameters without further reference to controls or actions, and without directly using the machinery of approximate Dynamic Programming and Reinforcement Learning. Here we derive simpler algorithms at the autonomous system level, and show that they compute the same quantities as policy gradients and Hessians, natural gradients, proximal methods. Analogs to approximate policy iteration and off-policy learning are also available. Since policy parameters and other system parameters are treated uniformly, the same algorithms apply to behavioral cloning, mechanism design, system identification, learning of state estimators. Tuning of generative AI models is not only possible, but is conceptually closer to the present framework than to Reinforcement Learning.

Composing Agents to Minimize Worst-case Risk

From software development to robot control, modern agentic systems decompose complex objectives into a sequence of subtasks and choose a set of specialized AI agents to complete them. We formalize an agentic workflow as a directed acyclic graph, called an agent graph, where edges represent AI agents and paths correspond to feasible compositions of agents. When deploying these systems in the real world, we need to choose compositions of agents that not only maximize the task success, but also minimize risk where the risk captures requirements like safety, fairness, and privacy. This additionally requires carefully analyzing the low-probability (tail) behaviors of compositions of agents. In this work, we consider worst-case risk minimization over the set of feasible agent compositions. We define worst-case risk as the tail quantile -- also known as value-at-risk -- of the loss distribution of the agent composition where the loss quantifies the risk associated with agent behaviors. We introduce an efficient algorithm that traverses the agent graph and finds a near-optimal composition of agents by approximating the value-at-risk via a union bound and dynamic programming. Furthermore, we prove that the approximation is near-optimal asymptotically for a broad class of practical loss functions. To evaluate our framework, we consider a suite of video game-like control benchmarks that require composing several agents trained with reinforcement learning and demonstrate our algorithm's effectiveness in approximating the value-at-risk and identifying the optimal agent composition.

Spectral Efficiency Maximization for DMA-enabled Multiuser MISO with Statistical CSI

Dynamic metasurface antennas (DMAs) offer the potential to achieve large-scale antenna arrays with low power consumption and reduced hardware costs, making them a promising technology for future communication systems. This paper investigates the spectral efficiency (SE) of DMA-enabled multiuser multiple-input single-output (MISO) systems in both uplink and downlink transmissions, using only statistical channel state information (CSI) to maximize the ergodic sum rate of multiple users. For the uplink system, we consider two decoding rules: minimum mean square error (MMSE) with and without successive interference cancellation (SIC). For both decoders, we derive closed-form surrogates to substitute the original expressions of ergodic sum rate and formulate tractable optimization problems for designing DMA weights. Then, a weighted MMSE (WMMSE)-based algorithm is proposed to maximize the ergodic sum rate. For the downlink system, we derive an approximate expression for the ergodic sum rate and formulate a hybrid analog/digital beamforming optimization problem that jointly optimizes the digital precoder and DMA weights. A penalty dual decomposition (PDD)-based algorithm is proposed by leveraging the fractional programming framework. Numerical results validate the accuracy of the derived surrogates and highlight the superiority of the proposed algorithms over baseline schemes. It is shown that these algorithms are effective across various DMA settings and are particularly well-suited for system design in fast time-varying channels.

Deep Learning for Continuous-time Stochastic Control with Jumps

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to approximate the value function. Leveraging a continuous-time version of the dynamic programming principle, we derive two different training objectives based on the Hamilton-Jacobi-Bellman equation, ensuring that the networks capture the underlying stochastic dynamics. Empirical evaluations on different problems illustrate the accuracy and scalability of our approach, demonstrating its effectiveness in solving complex, high-dimensional stochastic control tasks.