Abstract--Underwater environments pose significant challenges for visual Simultaneous Localization and Mapping (SLAM) systems due to limited visibility, inadequate illumination, and sporadic loss of structural features in images. Addressing these challenges, this paper introduces a novel, tightly-coupled Acoustic-Visual-Inertial SLAM approach, termed AQUA-SLAM, to fuse a Doppler Velocity Log (DVL), a stereo camera, and an Inertial Measurement Unit (IMU) within a graph optimization framework. The proposed system will be made open-source for the community. These vehicles are indispensable occasionally outside the camera's field of view leading to for tasks such as seabed mapping, pipeline and intermittent loss of visual tracking. Therefore, although visual cable inspections, biological and environmental monitoring, SLAM techniques have recently made tremendous progress and the maintenance of underwater infrastructure. A key in terrestrial settings [1], [2], [3], their performance and application area is the detailed visual inspection of subsea robustness are inevitably compromised in underwater due to structures, including offshore wind turbine foundations, where the complex and dynamic nature of aquatic environments. Considering cameras are widely equipped on underwater (IMU), known as visual-inertial SLAM (VI-SLAM) [4], [5], robots, visual Simultaneous Localization and Mapping can alleviate some of the challenges arising from transient, (SLAM) techniques emerge as natural solutions. The rapid attenuation of underwater SLAM systems, particularly against shortterm of light energy in water severely limits the visibility of visual disruptions, can be substantially enhanced [6]. However, most of the challenges for underwater vision, such Moreover, underwater vision often suffers from poor lighting as the limited visibility and the "marine snow", are longterm and blizzards of "marine snow" caused by small particles of effects that last at least from tens of seconds to a few organic matter in water, severely reducing image quality with minutes before being mitigated. VI-SLAM also encounters increased motion blur and dynamic image regions.

In online marketplaces, dynamic assortment selection and pricing for sequentially arriving buyers presents a challenge for online learning. Since the preferences of buyers are varying and uncertain, adaptive strategies are essential to meet their needs and maximize the effectiveness of offers. To address this problem, we investigate the application of online learning techniques for contextual assortment selection and pricing. Assortment selection involves the seller choosing a subset of items from a vast catalog to present to buyers, and dynamically assigning prices to the offered items. The overall goal is to maximize revenue over the course of repeated interactions. Dynamic assortment selection and pricing strategies are deployed in a variety of online sectors including e-commerce (e.g., Amazon), food delivery (e.g., Uber Eats), and hospitality (e.g., Airbnb). With similar systems becoming ubiquitous in our daily lives, there is a growing opportunity to deliver tailored product recommendations and pricing adjustments. Therefore, it is crucial to consider data-driven approaches that can enhance user experiences and boost profitability in today's highly competitive digital industry.

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology into the dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, yielding localized spectral topological filter frames. The learning problem is cast to jointly infer the underlying cell complex and optimize the dictionary coefficients and the sparse signal representation. We efficiently solve the problem via iterative alternating algorithms. Numerical results on both synthetic and real data show the effectiveness of the proposed procedure in jointly learning the sparse representations and the underlying relational structure of topological signals.

Inter-robot collisions pose a significant safety risk when multiple robotic arms operate in close proximity. We present an online collision avoidance methodology leveraging 3D convex shape-based High-Order Control Barrier Functions (HOCBFs) to address this issue. While prior works focused on using Control Barrier Functions (CBFs) for human-robotic arm and single-arm collision avoidance, we explore the problem of collision avoidance between multiple robotic arms operating in a shared space. In our methodology, we utilize the proposed HOCBFs as centralized and decentralized safety filters. These safety filters are compatible with any nominal controller and ensure safety without significantly restricting the robots' workspace. A key challenge in implementing these filters is the computational overhead caused by the large number of safety constraints and the computation of a Hessian matrix per constraint. We address this challenge by employing numerical differentiation methods to approximate computationally intensive terms. The effectiveness of our method is demonstrated through extensive simulation studies and real-world experiments with Franka Research 3 robotic arms.

Target search problems are central to a wide range of fields, from biological foraging to the optimization algorithms. Recently, the ability to reset the search has been shown to significantly improve the searcher's efficiency. However, the optimal resetting strategy depends on the specific properties of the search problem and can often be challenging to determine. In this work, we propose a reinforcement learning (RL)-based framework to train agents capable of optimizing their search efficiency in environments by learning how to reset. First, we validate the approach in a well-established benchmark: the Brownian search with resetting. There, RL agents consistently recover strategies closely resembling the sharp resetting distribution, known to be optimal in this scenario. We then extend the framework by allowing agents to control not only when to reset, but also their spatial dynamics through turning actions. In this more complex setting, the agents discover strategies that adapt both resetting and turning to the properties of the environment, outperforming the proposed benchmarks. These results demonstrate how reinforcement learning can serve both as an optimization tool and a mechanism for uncovering new, interpretable strategies in stochastic search processes with resetting.

The evaluation of fairness models in Machine Learning involves complex challenges, such as defining appropriate metrics, balancing trade-offs between utility and fairness, and there are still gaps in this stage. This work presents a novel multi-objective evaluation framework that enables the analysis of utility-fairness trade-offs in Machine Learning systems. The framework was developed using criteria from Multi-Objective Optimization that collect comprehensive information regarding this complex evaluation task. The assessment of multiple Machine Learning systems is summarized, both quantitatively and qualitatively, in a straightforward manner through a radar chart and a measurement table encompassing various aspects such as convergence, system capacity, and diversity. The framework's compact representation of performance facilitates the comparative analysis of different Machine Learning strategies for decision-makers, in real-world applications, with single or multiple fairness requirements. The framework is model-agnostic and flexible to be adapted to any kind of Machine Learning systems, that is, black- or white-box, any kind and quantity of evaluation metrics, including multidimensional fairness criteria. The functionality and effectiveness of the proposed framework is shown with different simulations, and an empirical study conducted on a real-world dataset with various Machine Learning systems.

Motion planning and trajectory generation are crucial technologies in various domains including the control of Unmanned Aerial Vehicles (UAV), manipulators, and rockets. However, optimization-based real-time motion planning becomes increasingly challenging due to the problem's probable non-convexity and the inherent limitations of Non-Linear Programming algorithms. Highly nonlinear dynamics, obstacle avoidance constraints, and non-convex inputs can exacerbate these difficulties. To address these hurdles, this paper proposes a two-layer optimization algorithm for 2D vehicles by dynamically reformulating small time horizon convex programming subproblems, aiming to provide real-time guarantees for trajectory optimization. Our approach involves breaking down the original problem into small horizon-based planning cycles with fixed final times, referred to as planning cycles. Each planning cycle is then solved within a series of restricted convex sets identified by our customized search algorithms incrementally. The key benefits of our proposed algorithm include fast computation speeds and lower task time. We demonstrate these advantages through mathematical proofs under some moderate preconditions and experimental results.

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper presents a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized GNE, expanding the solution space. We also propose a systematic approach for selecting the optimal GNE based on predefined criteria, enhancing practical flexibility. Numerical examples illustrate the methods effectiveness, offering an alternative to traditional normalized solutions.

We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by small isotropic normal noise. The addition of such noise may be interpreted as a stochastic form of sharpness-aware minimization (SAM) and we prove several results that relate its action on the underlying landscape and training dynamics to the sharpness of the loss. In particular, the noise changes the expected gradient to force balancing of the weight matrices at a fast rate along the descent trajectory. In the diagonal linear model, we show that this equates to minimizing the average sharpness, as well as the trace of the Hessian matrix, among all possible factorizations of the same matrix. Further, the noise forces the gradient descent iterates towards a shrinkage-thresholding of the underlying true parameter, with the noise level explicitly regulating both the shrinkage factor and the threshold.

In this paper, we propose a general and novel formulation of ranking and selection with the existence of streaming input data. The collection of multiple streams of such data may consume different types of resources, and hence can be conducted simultaneously. To utilize the streaming input data, we aggregate simulation outputs generated under heterogeneous input distributions over time to form a performance estimator. By characterizing the asymptotic behavior of the performance estimators, we formulate two optimization problems to optimally allocate budgets for collecting input data and running simulations. We then develop a multi-stage simultaneous budget allocation procedure and provide its statistical guarantees such as consistency and asymptotic normality. We conduct several numerical studies to demonstrate the competitive performance of the proposed procedure.