We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.

For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called "l0 norm" which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing sparsity when incorporated into an optimization problem. However, in big data settings wherein noisy estimates of the gradient must be evaluated out of computational necessity, the literature is scant on methods that reliably converge. In this paper we present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying stochastic process, and demonstrate the performance on two Machine Learning problems.

The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific applications. However, the essential geometric structure of the nonconvex robust phase retrieval based on the $\ell_1$-loss is largely unknown to study spurious local solutions, even under the ideal noiseless setting, and its intrinsic nonsmooth nature also impacts the efficiency of optimization algorithms. This paper introduces the smoothed robust phase retrieval (SRPR) based on a family of convolution-type smoothed loss functions. Theoretically, we prove that the SRPR enjoys a benign geometric structure with high probability: (1) under the noiseless situation, the SRPR has no spurious local solutions, and the target signals are global solutions, and (2) under the infrequent but arbitrary corruptions, we characterize the stationary points of the SRPR and prove its benign landscape, which is the first landscape analysis of phase retrieval with corruption in the literature. Moreover, we prove the local linear convergence rate of gradient descent for solving the SRPR under the noiseless situation. Experiments on both simulated datasets and image recovery are provided to demonstrate the numerical performance of the SRPR.

Learning-based methods have gained attention as general-purpose solvers because they can automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face challenges with scalability. To address these issues, the improved Sampling algorithm for Combinatorial Optimization (iSCO) using discrete Langevin dynamics has been proposed, demonstrating better performance than several learning-based solvers. This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA). QQA smoothly transitions the objective function from a simple convex form, where half-integral solutions dominate, to the original objective function, where the variables are restricted to 0 or 1. Furthermore, we incorporate parallel run communication leveraging GPUs, enhancing exploration capabilities and accelerating convergence. Numerical experiments demonstrate that our approach is a competitive general-purpose solver, achieving comparable performance to iSCO across various benchmark problems. Notably, our method exhibits superior trade-offs between speed and solution quality for large-scale instances compared to iSCO, commercial solvers, and specialized algorithms.

Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter. While DD has a wide range of applications, the theory supporting it is less well evolved. New methods of DD are compared on a common set of benchmarks, rather than oriented towards any particular learning task. In this work, we present a formal model of DD, arguing that a precise characterization of the underlying optimization problem must specify the inference task associated with the application of interest. Without this task-specific focus, the DD problem is under-specified, and the selection of a DD algorithm for a particular task is merely heuristic. Our formalization reveals novel applications of DD across different modeling environments. We analyze existing DD methods through this broader lens, highlighting their strengths and limitations in terms of accuracy and faithfulness to optimal DD operation. Finally, we present numerical results for two case studies important in contemporary settings. Firstly, we address a critical challenge in medical data analysis: merging the knowledge from different datasets composed of intersecting, but not identical, sets of features, in order to construct a larger dataset in what is usually a small sample setting. Secondly, we consider out-of-distribution error across boundary conditions for physics-informed neural networks (PINNs), showing the potential for DD to provide more physically faithful data. By establishing this general formulation of DD, we aim to establish a new research paradigm by which DD can be understood and from which new DD techniques can arise.

We address a control system optimization problem that arises in multi-class, multi-server queueing system scheduling with uncertainty. In this scenario, jobs incur holding costs while awaiting completion, and job-server assignments yield observable stochastic rewards with unknown mean values. The rewards for job-server assignments are assumed to follow a bilinear model with respect to features characterizing jobs and servers. Our objective is regret minimization, aiming to maximize the cumulative reward of job-server assignments over a time horizon while maintaining a bounded total job holding cost, thus ensuring queueing system stability. This problem is motivated by applications in computing services and online platforms. To address this problem, we propose a scheduling algorithm based on weighted proportional fair allocation criteria augmented with marginal costs for reward maximization, incorporating a bandit strategy. Our algorithm achieves sub-linear regret and sub-linear mean holding cost (and queue length bound) with respect to the time horizon, thus guaranteeing queueing system stability. Additionally, we establish stability conditions for distributed iterative algorithms for computing allocations, which are relevant to large-scale system applications. Finally, we validate the efficiency of our algorithm through numerical experiments.

Recent research has indicated a substantial rise in interest in understanding Nesterov's accelerated gradient methods via their continuous-time models. However, most existing studies focus on specific classes of Nesterov's methods, which hinders the attainment of an in-depth understanding and a unified perspective. To address this deficit, we present generalized continuous-time models that cover a broad range of Nesterov's methods, including those previously studied under existing continuous-time frameworks. Our key contributions are as follows. First, we identify the convergence rates of the generalized models, eliminating the need to determine the convergence rate for any specific continuous-time model derived from them. Second, we show that six existing continuous-time models are special cases of our generalized models, thereby positioning our framework as a unifying tool for analyzing and understanding these models. Third, we design a restart scheme for Nesterov's methods based on our generalized models and show that it ensures a monotonic decrease in objective function values. Owing to the broad applicability of our models, this scheme can be used to a broader class of Nesterov's methods compared to the original restart scheme. Fourth, we uncover a connection between our generalized models and gradient flow in continuous time, showing that the accelerated convergence rates of our generalized models can be attributed to a time reparametrization in gradient flow. Numerical experiment results are provided to support our theoretical analyses and results.

Training social event detection models through federated learning (FedSED) aims to improve participants' performance on the task. However, existing federated learning paradigms are inadequate for achieving FedSED's objective and exhibit limitations in handling the inherent heterogeneity in social data. This paper proposes a personalized federated learning framework with a dual aggregation mechanism for social event detection, namely DAMe. We present a novel local aggregation strategy utilizing Bayesian optimization to incorporate global knowledge while retaining local characteristics. Moreover, we introduce a global aggregation strategy to provide clients with maximum external knowledge of their preferences. In addition, we incorporate a global-local event-centric constraint to prevent local overfitting and ``client-drift''. Experiments within a realistic simulation of a natural federated setting, utilizing six social event datasets spanning six languages and two social media platforms, along with an ablation study, have demonstrated the effectiveness of the proposed framework. Further robustness analyses have shown that DAMe is resistant to injection attacks.

In this survey, we design formal verification and control algorithms for autonomous systems with practical safety guarantees using conformal prediction (CP), a statistical tool for uncertainty quantification. We focus on learning-enabled autonomous systems (LEASs) in which the complexity of learning-enabled components (LECs) is a major bottleneck that hampers the use of existing model-based verification and design techniques. Instead, we advocate for the use of CP, and we will demonstrate its use in formal verification, systems and control theory, and robotics. We argue that CP is specifically useful due to its simplicity (easy to understand, use, and modify), generality (requires no assumptions on learned models and data distributions, i.e., is distribution-free), and efficiency (real-time capable and accurate). We pursue the following goals with this survey. First, we provide an accessible introduction to CP for non-experts who are interested in using CP to solve problems in autonomy. Second, we show how to use CP for the verification of LECs, e.g., for verifying input-output properties of neural networks. Third and fourth, we review recent articles that use CP for safe control design as well as offline and online verification of LEASs. We summarize their ideas in a unifying framework that can deal with the complexity of LEASs in a computationally efficient manner. In our exposition, we consider simple system specifications, e.g., robot navigation tasks, as well as complex specifications formulated in temporal logic formalisms. Throughout our survey, we compare to other statistical techniques (e.g., scenario optimization, PAC-Bayes theory, etc.) and how these techniques have been used in verification and control. Lastly, we point the reader to open problems and future research directions.

The next-generation radio access network (RAN), known as Open RAN, is poised to feature an AI-native interface for wireless cellular networks, including emerging satellite-terrestrial systems, making deep learning integral to its operation. In this paper, we address the nonconvex optimization challenge of joint subcarrier and power allocation in Open RAN, with the objective of minimizing the total power consumption while ensuring users meet their transmission data rate requirements. We propose OpenRANet, an optimization-based deep learning model that integrates machine-learning techniques with iterative optimization algorithms. We start by transforming the original nonconvex problem into convex subproblems through decoupling, variable transformation, and relaxation techniques. These subproblems are then efficiently solved using iterative methods within the standard interference function framework, enabling the derivation of primal-dual solutions. These solutions integrate seamlessly as a convex optimization layer within OpenRANet, enhancing constraint adherence, solution accuracy, and computational efficiency by combining machine learning with convex analysis, as shown in numerical experiments. OpenRANet also serves as a foundation for designing resource-constrained AI-native wireless optimization strategies for broader scenarios like multi-cell systems, satellite-terrestrial networks, and future Open RAN deployments with complex power consumption requirements.