Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs generally involves addressing a complex robust optimization problem, which can be intractable. Scenario-based methods have been proposed to simplify this computation. Then, one needs to verify if the CBF actually satisfies the robust constraints. We present an approach to perform this verification that relies on Lipschitz arguments, and forms the basis of a certification algorithm designed for sample efficiency. Through a numerical example, we validated the efficiency of the proposed procedure.

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

Department of Physics, Arizona State University, Tempe, Arizona 85287, USA (Dated: September 5, 2025) Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and measurement errors, we show that for many chaotic systems, widely used sparse-optimization methods for discovering governing equations produce models that depend sensitively on the measurement procedure, yet all such models generate virtually identical chaotic attractors, leading to a striking limitation that challenges the conventional notion of equation-based modeling in complex dynamical systems. Calculating the Koopman spectra, we find that the different sets of equations agree in their large eigenvalues and the differences begin to appear when the eigenvalues are smaller than an equation-dependent threshold. The results suggest that finding the governing equations of the system and attempting to interpret them physically may lead to misleading conclusions. It would be more useful to work directly with the available data using, e.g., machine-learning methods. In physical science, a methodology of biblical importance is developing a quantitative model by extracting a set of governing equations from experimental data.

--Federated learning (FL) effectively promotes collaborative training among distributed clients with privacy considerations in the Internet of Things (IoT) scenarios. Despite of data heterogeneity, FL clients may also be constrained by limited energy and availability budgets. Therefore, effective selection of clients participating in training is of vital importance for the convergence of the global model and the balance of client contributions. In this paper, we discuss the performance impact of client availability with time-series data on federated learning. We set up three different scenarios that affect the availability of time-series data and propose FedDeCAB, a novel, semi-decentralized client selection method applying probabilistic rankings of available clients. When a client is disconnected from the server, FedDeCAB allows obtaining partial model parameters from the nearest neighbor clients for joint optimization, improving the performance of offline models and reducing communication overhead. Experiments based on real-world large-scale taxi and vessel trajectory datasets show that FedDeCAB is effective under highly heterogeneous data distribution, limited communication budget, and dynamic client offline or rejoining. Traditional machine learning (ML) requires the central server to gather data from various node devices for model training. However, the access to personal data from edge devices is usually subject to privacy restrictions and the large scale of local data in common edge computing environments or scenarios with a large number of Internet of Things (IoT) devices.

In the context of continuously rising global air traffic, efficient and safe Conflict Detection and Resolution (CD&R) is paramount for air traffic management. Although Deep Reinforcement Learning (DRL) offers a promising pathway for CD&R automation, existing approaches commonly suffer from a "unimodal bias" in their policies. This leads to a critical lack of decision-making flexibility when confronted with complex and dynamic constraints, often resulting in "decision deadlocks." To overcome this limitation, this paper pioneers the integration of diffusion probabilistic models into the safety-critical task of CD&R, proposing a novel autonomous conflict resolution framework named Diffusion-AC. Diverging from conventional methods that converge to a single optimal solution, our framework models its policy as a reverse denoising process guided by a value function, enabling it to generate a rich, high-quality, and multimodal action distribution. This core architecture is complemented by a Density-Progressive Safety Curriculum (DPSC), a training mechanism that ensures stable and efficient learning as the agent progresses from sparse to high-density traffic environments. Extensive simulation experiments demonstrate that the proposed method significantly outperforms a suite of state-of-the-art DRL benchmarks. Most critically, in the most challenging high-density scenarios, Diffusion-AC not only maintains a high success rate of 94.1% but also reduces the incidence of Near Mid-Air Collisions (NMACs) by approximately 59% compared to the next-best-performing baseline, significantly enhancing the system's safety margin. This performance leap stems from its unique multimodal decision-making capability, which allows the agent to flexibly switch to effective alternative maneuvers.

We investigate partially identifiable queries in a class of causal models. We focus on acyclic Structural Causal Models that are quasi-Markovian (that is, each endogenous variable is connected with at most one exogenous confounder). We look into scenarios where endogenous variables are observed (and a distribution over them is known), while exogenous variables are not fully specified. This leads to a representation that is in essence a Bayesian network where the distribution of root variables is not uniquely determined. In such circumstances, it may not be possible to precisely compute a probability value of interest. We thus study the computation of tight probability bounds, a problem that has been solved by multilinear programming in general, and by linear programming when a single confounded component is intervened upon. We present a new algorithm to simplify the construction of such programs by exploiting input probabilities over endogenous variables. For scenarios with a single intervention, we apply column generation to compute a probability bound through a sequence of auxiliary linear integer programs, thus showing that a representation with polynomial cardinality for exogenous variables is possible. Experiments show column generation techniques to be superior to existing methods.

This paper presents a Segmented Trajectory Optimization (STO) method for autonomous parking, which refines an initial trajectory into a dynamically feasible and collision-free one using an iterative SQP-based approach. STO maintains the maneuver strategy of the high-level global planner while allowing curvature discontinuities at switching points to improve maneuver efficiency. To ensure safety, a convex corridor is constructed via GJK-accelerated ellipse shrinking and expansion, serving as safety constraints in each iteration. Numerical simulations in perpendicular and reverse-angled parking scenarios demonstrate that STO enhances maneuver efficiency while ensuring safety. Moreover, computational performance confirms its practicality for real-world applications.

Online 3D Bin Packing Problem (3D-BPP) has widespread applications in industrial automation. Existing methods usually solve the problem with limited resolution of spatial discretization, and/or cannot deal with complex practical constraints well. We propose to enhance the practical applicability of online 3D-BPP via learning on a novel hierarchical representation, packing configuration tree (PCT). PCT is a full-fledged description of the state and action space of bin packing which can support packing policy learning based on deep reinforcement learning (DRL). The size of the packing action space is proportional to the number of leaf nodes, making the DRL model easy to train and well-performing even with continuous solution space. We further discover the potential of PCT as tree-based planners in deliberately solving packing problems of industrial significance, including large-scale packing and different variations of BPP setting. A recursive packing method is proposed to decompose large-scale packing into smaller sub-trees while a spatial ensemble mechanism integrates local solutions into global. For different BPP variations with additional decision variables, such as lookahead, buffering, and offline packing, we propose a unified planning framework enabling out-of-the-box problem solving. Extensive evaluations demonstrate that our method outperforms existing online BPP baselines and is versatile in incorporating various practical constraints. The planning process excels across large-scale problems and diverse problem variations. We develop a real-world packing robot for industrial warehousing, with careful designs accounting for constrained placement and transportation stability. Our packing robot operates reliably and efficiently on unprotected pallets at 10 seconds per box. It achieves averagely 19 boxes per pallet with 57.4% space utilization for relatively large-size boxes.

We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for adaptively tuning the proximal term. It allows the penalty parameter to grow rapidly in the early stages to speed up progress, while ameliorating the issue of ill-conditioning in later iterations, a well-known drawback of the traditional approach of linearly increasing the penalty parameters. A key element in our analysis lies in the observation that the augmented Lagrangian can be controlled effectively along the iterates, provided an initial feasible point is available. Our analysis, while simple, provides a new theoretical perspective about P-ALM and, as a by-product, results in similar convergence properties for its non-proximal variant, the classical augmented Lagrangian method (ALM). Numerical experiments, including convex and nonconvex problem instances, demonstrate the effectiveness of our approach.

This paper studies the complexity of finding an $ε$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order method, F${}^2$SA, achieving the $\tilde{\mathcal{O}}(ε^{-6})$ upper complexity bound for first-order smooth problems. This is slower than the optimal $Ω(ε^{-4})$ complexity lower bound in its single-level counterpart. In this work, we show that faster rates are achievable for higher-order smooth problems. We first reformulate F$^2$SA as approximating the hyper-gradient with a forward difference. Based on this observation, we propose a class of methods F${}^2$SA-$p$ that uses $p$th-order finite difference for hyper-gradient approximation and improves the upper bound to $\tilde{\mathcal{O}}(p ε^{4-p/2})$ for $p$th-order smooth problems. Finally, we demonstrate that the $Ω(ε^{-4})$ lower bound also holds for stochastic bilevel problems when the high-order smoothness holds for the lower-level variable, indicating that the upper bound of F${}^2$SA-$p$ is nearly optimal in the highly smooth region $p = Ω( \log ε^{-1} / \log \log ε^{-1})$.