Motivated by the APCG method for empirical risk minimization, this paper proposed an an accelerated decentralized stochastic algorithm for finite sums. An augmented communication graph is proposed such that the original constrained optimization problem can be transformed to its dual formulation, which can be solved by stochastic coordinate descent. The proposed method employs randomized pairwise communication and stochastic computation. An adaptive sampling scheme for selecting edge is introduced, which is analogous to importance sampling in the literature. The theoretical analysis shows that the proposed algorithm achieves an optimal linear convergence rate for finite-sums, and the time complexity is better than the existing results.

Summary and Contributions: This paper describes a way to smooth functions that interpolates between the Moreau envelope and the "randomized sampling" smoothing which approximates a function f with fRS(x) E_z[f(x gamma z)] where is a standard Gaussian and gamma is a smoothing parameter. Such an approach is useful because many optimization methods only apply to smooth functions, but can be extended to nonsmooth functions with controlled error by using such smoothings. The key claimed drawback with random sampling is that it introduces an approximation error for a given level of smoothing that is dimension-dependent (on the order of sqrt(d)). The key claimed drawback with the Moreau envelope is that it is difficult to compute (as it involves solving an optimization problem). The proposed interpolation essentially replaces the minimization problem in the Moreau envelope with a "soft" approximation.

As opposed to conventional training methods tailored to minimize a given statistical metric or task-agnostic loss (e.g., mean squared error), Decision-Focused Learning (DFL) trains machine learning models for optimal performance in downstream decision-making tools. We argue that DFL can be leveraged to learn the parameters of system dynamics, expressed as constraint of the convex optimization control policy, while the system control signal is being optimized, thus creating an end-to-end learning framework. This is particularly relevant for systems in which behavior changes once the control policy is applied, hence rendering historical data less applicable. The proposed approach can perform system identification - i.e., determine appropriate parameters for the system analytical model - and control simultaneously to ensure that the model's accuracy is focused on areas most relevant to control. Furthermore, because black-box systems are non-differentiable, we design a loss function that requires solely to measure the system response. We propose pre-training on historical data and constraint relaxation to stabilize the DFL and deal with potential infeasibilities in learning. We demonstrate the usefulness of the method on a building Heating, Ventilation, and Air Conditioning day-ahead management system for a realistic 15-zone building located in Denver, US. The results show that the conventional RC building model, with the parameters obtained from historical data using supervised learning, underestimates HVAC electrical power consumption. For our case study, the ex-post cost is on average six times higher than the expected one. Meanwhile, the same RC model with parameters obtained via DFL underestimates the ex-post cost only by 3%.

This article proposes an active-learning-based adaptive trajectory tracking control method for autonomous ground vehicles to compensate for modeling errors and unmodeled dynamics. The nominal vehicle model is decoupled into lateral and longitudinal subsystems, which are augmented with online Gaussian Processes (GPs), using measurement data. The estimated mean functions of the GPs are used to construct a feedback compensator, which, together with an LPV state feedback controller designed for the nominal system, gives the adaptive control structure. To assist exploration of the dynamics, the paper proposes a new, dynamic active learning method to collect the most informative samples to accelerate the training process. To analyze the performance of the overall learning tool-chain provided controller, a novel iterative, counterexample-based algorithm is proposed for calculating the induced L2 gain between the reference trajectory and the tracking error. The analysis can be executed for a set of possible realizations of the to-be-controlled system, giving robust performance certificate of the learning method under variation of the vehicle dynamics. The efficiency of the proposed control approach is shown on a high-fidelity physics simulator and in real experiments using a 1/10 scale F1TENTH electric car.

Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential for ensuring accurate and effective clustering, making graph structure learning (GSL) central for enhancing spectral clustering performance in response to the growing demand for scalable solutions. Despite advancements in GSL, there is a lack of comprehensive surveys specifically addressing its role within spectral clustering. To bridge this gap, this survey presents a comprehensive review of spectral clustering methods, emphasizing on the critical role of GSL. We explore various graph construction techniques, including pairwise, anchor, and hypergraph-based methods, in both fixed and adaptive settings. Additionally, we categorize spectral clustering approaches into single-view and multi-view frameworks, examining their applications within one-step and two-step clustering processes. We also discuss multi-view information fusion techniques and their impact on clustering data. By addressing current challenges and proposing future research directions, this survey provides valuable insights for advancing spectral clustering methodologies and highlights the pivotal role of GSL in tackling large-scale and high-dimensional data clustering tasks.

Wireless positioning technologies hold significant value for applications in autonomous driving, extended reality (XR), unmanned aerial vehicles (UAVs), and more. With the advancement of artificial intelligence (AI), leveraging AI to enhance positioning accuracy and robustness has emerged as a field full of potential. Driven by the requirements and functionalities defined in the 3rd Generation Partnership Project (3GPP) standards, AI/machine learning (ML)-based positioning is becoming a key technology to overcome the limitations of traditional methods. This paper begins with an introduction to the fundamentals of AI and wireless positioning, covering AI models, algorithms, positioning applications, emerging wireless technologies, and the basics of positioning techniques. Subsequently, focusing on standardization progress, we provide a comprehensive review of the evolution of 3GPP positioning standards, with an emphasis on the integration of AI/ML technologies in recent and upcoming releases. Based on the AI/ML-assisted positioning and direct AI/ML positioning schemes outlined in the standards, we conduct an in-depth investigation of related research. we focus on state-of-the-art (SOTA) research in AI-based line-of-sight (LOS)/non-line-of-sight (NLOS) detection, time of arrival (TOA)/time difference of arrival (TDOA) estimation, and angle estimation techniques. For Direct AI/ML Positioning, we explore SOTA advancements in fingerprint-based positioning, knowledge-assisted AI positioning, and channel charting-based positioning. Furthermore, we introduce publicly available datasets for wireless positioning and conclude by summarizing the challenges and opportunities of AI-driven wireless positioning.

As data sets grow in size and complexity, it is becoming more difficult to pull useful features from them using hand-crafted feature extractors. For this reason, deep learning (DL) frameworks are now widely popular. The Holy Grail of DL and one of the most mysterious challenges in all of modern ML is to develop a fundamental understanding of DL optimization and generalization. While numerous optimization techniques have been introduced in the literature to navigate the exploration of the highly non-convex DL optimization landscape, many survey papers reviewing them primarily focus on summarizing these methodologies, often overlooking the critical theoretical analyses of these methods. In this paper, we provide an extensive summary of the theoretical foundations of optimization methods in DL, including presenting various methodologies, their convergence analyses, and generalization abilities. This paper not only includes theoretical analysis of popular generic gradient-based first-order and second-order methods, but it also covers the analysis of the optimization techniques adapting to the properties of the DL loss landscape and explicitly encouraging the discovery of well-generalizing optimal points. Additionally, we extend our discussion to distributed optimization methods that facilitate parallel computations, including both centralized and decentralized approaches. We provide both convex and non-convex analysis for the optimization algorithms considered in this survey paper. Finally, this paper aims to serve as a comprehensive theoretical handbook on optimization methods for DL, offering insights and understanding to both novice and seasoned researchers in the field.

We aim to redefine robust ego-motion estimation and photorealistic 3D reconstruction by addressing a critical limitation: the reliance on noise-free data in existing models. While such sanitized conditions simplify evaluation, they fail to capture the unpredictable, noisy complexities of real-world environments. Dynamic motion, sensor imperfections, and synchronization perturbations lead to sharp performance declines when these models are deployed in practice, revealing an urgent need for frameworks that embrace and excel under real-world noise. To bridge this gap, we tackle three core challenges: scalable data generation, comprehensive benchmarking, and model robustness enhancement. First, we introduce a scalable noisy data synthesis pipeline that generates diverse datasets simulating complex motion, sensor imperfections, and synchronization errors. Second, we leverage this pipeline to create Robust-Ego3D, a benchmark rigorously designed to expose noise-induced performance degradation, highlighting the limitations of current learning-based methods in ego-motion accuracy and 3D reconstruction quality. Third, we propose Correspondence-guided Gaussian Splatting (CorrGS), a novel test-time adaptation method that progressively refines an internal clean 3D representation by aligning noisy observations with rendered RGB-D frames from clean 3D map, enhancing geometric alignment and appearance restoration through visual correspondence. Extensive experiments on synthetic and real-world data demonstrate that CorrGS consistently outperforms prior state-of-the-art methods, particularly in scenarios involving rapid motion and dynamic illumination.

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.