We study the safe linear bandit problem, where an agent sequentially selects actions from a convex domain to maximize an unknown objective while ensuring unknown linear constraints are satisfied on a per-round basis. Existing approaches primarily rely on optimism-based methods with frequentist confidence bounds, often leading to computationally expensive action selection routines. We propose COnstrained Linear Thompson Sampling (COLTS), a sampling-based framework that efficiently balances regret minimization and constraint satisfaction by selecting actions on the basis of noisy perturbations of the estimates of the unknown objective vector and constraint matrix. We introduce three variants of COLTS, distinguished by the learner's available side information: - S-COLTS assumes access to a known safe action and ensures strict constraint enforcement by combining the COLTS approach with a rescaling towards the safe action. For $d$-dimensional actions, this yields $\tilde{O}(\sqrt{d^3 T})$ regret and zero constraint violations (or risk). - E-COLTS enforces constraints softly under Slater's condition, and attains regret and risk of $\tilde{O}(\sqrt{d^3 T})$ by combining COLTS with uniform exploration. - R-COLTS requires no side information, and ensures instance-independent regret and risk of $\tilde{O}(\sqrt{d^3 T})$ by leveraging repeated resampling. A key technical innovation is a coupled noise design, which maintains optimism while preserving computational efficiency, which is combined with a scaling based analysis technique to address the variation of the per-round feasible region induced by sampled constraint matrices. Our methods match the regret bounds of prior approaches, while significantly reducing computational costs compared to them, thus yielding a scalable and practical approach for constrained bandit linear optimization.

--In this paper we introduce MLINE-VINS, a novel monocular visual-inertial odometry (VIO) system that leverages line features and Manhattan Word assumption. Specifically, for line matching process, we propose a novel geometric line optical flow algorithm that efficiently tracks line features with varying lengths, whitch is do not require detections and descriptors in every frame. T o address the instability of Manhattan estimation from line features, we propose a tracking-by-detection module that consistently tracks and optimizes Manhattan framse in consecutive images. By aligning the Manhattan World with the VIO world frame, the tracking could restart using the latest pose from back-end, simplifying the coordinate transformations within the system. Furthermore, we implement a mechanism to validate Manhattan frames and a novel global structural constraints back-end optimization. Extensive experiments results on vairous datasets, including benchmark and self-collected datasets, show that the proposed approach outperforms existing methods in terms of accuracy and long-range robustness. CCURACY of pose estimation is a critical factor in various fields, such as autonomous driving, augmented reality, and robotics. Simultaneous localization and mapping (SLAM) has proven to be an effective approach to address this challenge [1], [2]. Among SLAM techniques, visual-inertial odometry (VIO) is particularly popular due to its cost-effectiveness, accuracy, and robustness. In VIO, point feature is widely used for camera pose estimation due to its simplicity and efficiency. Representative point-based VIO systems include MSCKF-VIO [3], OK-VINS [4] and VINS-MONO [5], with VINS-MONO being one of the most widely adopted algorithm. However, the performance of point-based VIO is affected by the number and spatial distribution of points and it significantly hindered in textureless environments, where the lack of texture leads to point loss. To address these limitations, line features are increasingly considered as a valuable complement to point features improving the robustness of VIO systems. Line features arecommonly found in low-texture environments, particularly in man-made environments [6].

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

With the advancements in modern intelligent technologies, mobile robots equipped with manipulators are increasingly operating in unstructured environments. These robots can plan sequences of actions for long-horizon tasks based on perceived information. However, in practice, the planned actions often fail due to discrepancies between the perceptual information used for planning and the actual conditions. In this paper, we introduce the {\itshape Conditional Subtree} (CSubBT), a general self-adjusting execution framework for mobile manipulation tasks based on Behavior Trees (BTs). CSubBT decomposes symbolic action into sub-actions and uses BTs to control their execution, addressing any potential anomalies during the process. CSubBT treats common anomalies as constraint non-satisfaction problems and continuously guides the robot in performing tasks by sampling new action parameters in the constraint space when anomalies are detected. We demonstrate the robustness of our framework through extensive manipulation experiments on different platforms, both in simulation and real-world settings.

Achieving real-time SLAM on mobile robotic systems with limited computational resources is challenging because the complexity of SLAM algorithms increases over time. This restriction can be lifted by offloading computations to edge servers, forming the emerging paradigm of edge-assisted SLAM. Nevertheless, the exogenous and stochastic input processes affect the dynamics of the edge-assisted SLAM system. Moreover, the requirements of clients on SLAM metrics change over time, exerting implicit and time-varying effects on the system. In this paper, we aim to push the limit beyond existing edge-assist SLAM by proposing a new architecture that can handle the input-driven processes and also satisfy clients' implicit and time-varying requirements. The key innovations of our work involve a regional feature prediction method for importance-aware local data processing, a configuration adaptation policy that integrates data compression/decompression and task offloading, and an input-dependent learning framework for task scheduling with constraint satisfaction. Extensive experiments prove that our architecture improves pose estimation accuracy and saves up to 47% of communication costs compared with a popular edge-assisted SLAM system, as well as effectively satisfies the clients' requirements. Index Terms --Simultaneous localization and mapping (SLAM), mobile edge computing (MEC), task offloading, task scheduling, and constrained reinforcement learning.

In Reinforcement Learning (RL), tasks with instantaneous hard constraints present significant challenges, particularly when the decision space is non-convex or non-star-convex. This issue is especially relevant in domains like autonomous vehicles and robotics, where constraints such as collision avoidance often take a non-convex form. In this paper, we establish a regret bound of $\tilde{\mathcal{O}}\bigl(\bigl(1 + \tfrac{1}{\tau}\bigr) \sqrt{\log(\tfrac{1}{\tau}) d^3 H^4 K} \bigr)$, applicable to both star-convex and non-star-convex cases, where $d$ is the feature dimension, $H$ the episode length, $K$ the number of episodes, and $\tau$ the safety threshold. Moreover, the violation of safety constraints is zero with high probability throughout the learning process. A key technical challenge in these settings is bounding the covering number of the value-function class, which is essential for achieving value-aware uniform concentration in model-free function approximation. For the star-convex setting, we develop a novel technique called Objective Constraint-Decomposition (OCD) to properly bound the covering number. This result also resolves an error in a previous work on constrained RL. In non-star-convex scenarios, where the covering number can become infinitely large, we propose a two-phase algorithm, Non-Convex Safe Least Squares Value Iteration (NCS-LSVI), which first reduces uncertainty about the safe set by playing a known safe policy. After that, it carefully balances exploration and exploitation to achieve the regret bound. Finally, numerical simulations on an autonomous driving scenario demonstrate the effectiveness of NCS-LSVI.

We study the application of emerging photonic and quantum computing architectures to solving the Traveling Salesman Problem (TSP), a well-known NP-hard optimization problem. We investigate several approaches: Simulated Annealing (SA), Quadratic Unconstrained Binary Optimization (QUBO-Ising) methods implemented on quantum annealers and Optical Coherent Ising Machines, as well as the Quantum Approximate Optimization Algorithm (QAOA) and the Quantum Phase Estimation (QPE) algorithm on gate-based quantum computers. QAOA and QPE were tested on the IBM Quantum platform. The QUBO-Ising method was explored using the D-Wave quantum annealer, which operates on superconducting Josephson junctions, and the QCI Dirac machine, a nonlinear optoelectronic Ising machine. Gate-based quantum computers demonstrated accurate results for small TSP instances in simulation. However, real quantum devices are hindered by noise and limited scalability. Circuit complexity grows with problem size, restricting performance to TSP instances with a maximum of 6 nodes. In contrast, Ising-based architectures show improved scalability for larger problem sizes. SQUID-based Ising machines can handle TSP instances with up to 12 nodes, while nonlinear optoelectronic Ising machines extend this capability to 18 nodes. Nevertheless, the solutions tend to be suboptimal due to hardware limitations and challenges in achieving ground state convergence as the problem size increases. Despite these limitations, Ising machines demonstrate significant time advantages over classical methods, making them a promising candidate for solving larger-scale TSPs efficiently.

Projection-based algorithms for constrained Online Convex Optimization (COCO) face scalability challenges in high-dimensional settings due to the computational complexity of projecting iterates onto constraint sets. This paper introduces a projection-free algorithm for COCO that achieves state-of-the-art performance guarantees while eliminating the need for projections. By integrating a separation oracle with adaptive Online Gradient Descent (OGD) and employing a Lyapunov-driven surrogate function, while dynamically adjusting step sizes using gradient norms, our method jointly optimizes the regret and cumulative constraint violation (CCV). We also use a blocked version of OGD that helps achieve tradeoffs betweeen the regret and CCV with the number of calls to the separation oracle. For convex cost functions, our algorithm attains an optimal regret of $\mathcal{O}(\sqrt{T})$ and a CCV of $\mathcal{O}(\sqrt{T} \log T)$, matching the best-known projection-based results, while only using $\tilde{\mathcal{O}}({T})$ calls to the separation oracle. The results also demonstrate a tradeoff where lower calls to the separation oracle increase the regret and the CCV. In the strongly convex setting, we further achieve a regret of $\mathcal{O}(\log T)$ and a CCV of $\mathcal{O}(\sqrt{T\log T} )$, while requiring ${\mathcal{O}}({T}^2)$ calls to the separation oracle. Further, tradeoff with the decreasing oracle calls is studied. These results close the gap between projection-free and projection-based approaches, demonstrating that projection-free methods can achieve performance comparable to projection-based counterparts.

NP-hard problems are assumed to be computationally intractable, meaning that no efficient (polynomial time) algorithm is guaranteed to correctly solve every input instance. One way of coping with NP-hardness is via the use of reliable heuristics. These are efficient algorithms that might not solve every input instance, but when they claim a solution, the solution is guaranteed to be correct. Consider the canonical NP-complete problem of SAT (determining whether a Boolean formula of the form (x1 x2 x3) (x2 x4) . . . A heuristic for finding satisfying assignments will naturally be reliable, because one can efficiently check whether the assignment found indeed satisfies all clauses of the input formula.

There is growing interest in utilizing large language models (LLMs) as co-pilots for combinatorial optimization and constraint programming tasks across various problems. This paper aims to advance this line of research by introducing Text2Zinc}, a cross-domain dataset for capturing optimization and satisfaction problems specified in natural language text. Our work is distinguished from previous attempts by integrating both satisfaction and optimization problems within a unified dataset using a solver-agnostic modeling language. To achieve this, we leverage MiniZinc's solver-and-paradigm-agnostic modeling capabilities to formulate these problems. Using the Text2Zinc dataset, we conduct comprehensive baseline experiments to compare execution and solution accuracy across several methods, including off-the-shelf prompting strategies, chain-of-thought reasoning, and a compositional approach. Additionally, we explore the effectiveness of intermediary representations, specifically knowledge graphs. Our findings indicate that LLMs are not yet a push-button technology to model combinatorial problems from text. We hope that Text2Zinc serves as a valuable resource for researchers and practitioners to advance the field further.