The emergence of 3D Gaussian Splatting (3DGS) has recently sparked a renewed wave of dense visual SLAM research. However, current methods face challenges such as sensitivity to artifacts and noise, sub-optimal selection of training viewpoints, and a lack of light global optimization. In this paper, we propose a dense SLAM system that tightly couples 3DGS with ORB features. We design a joint optimization approach for robust tracking and effectively reducing the impact of noise and artifacts. This involves combining novel geometric observations, derived from accumulated transmittance, with ORB features extracted from pixel data. Furthermore, to improve mapping quality, we propose an adaptive Gaussian expansion and regularization method that enables Gaussian primitives to represent the scene compactly. This is coupled with a viewpoint selection strategy based on the hybrid graph to mitigate over-fitting effects and enhance convergence quality. Finally, our approach achieves compact and high-quality scene representations and accurate localization. GSORB-SLAM has been evaluated on different datasets, demonstrating outstanding performance. The code will be available.

We consider fair resource allocation in sequential decision-making environments modeled as weakly coupled Markov decision processes, where resource constraints couple the action spaces of $N$ sub-Markov decision processes (sub-MDPs) that would otherwise operate independently. We adopt a fairness definition using the generalized Gini function instead of the traditional utilitarian (total-sum) objective. After introducing a general but computationally prohibitive solution scheme based on linear programming, we focus on the homogeneous case where all sub-MDPs are identical. For this case, we show for the first time that the problem reduces to optimizing the utilitarian objective over the class of "permutation invariant" policies. This result is particularly useful as we can exploit Whittle index policies in the restless bandits setting while, for the more general setting, we introduce a count-proportion-based deep reinforcement learning approach. Finally, we validate our theoretical findings with comprehensive experiments, confirming the effectiveness of our proposed method in achieving fairness.

This work establishes a solution to the problem of assessing the robustness of multi-object assemblies to external forces. Our physically-grounded approach handles arbitrary static structures made from rigid objects of any shape and mass distribution without relying on heuristics or approximations. The result is a method that provides a foundation for autonomous robot decision-making when interacting with objects in frictional contact. Our strategy decouples slipping from toppling, enabling independent assessments of these two phenomena, with a shared robustness representation being key to combining the results into an accurate robustness assessment. Our algorithms can be used by motion planners to produce efficient assembly transportation plans, and by object placement planners to select poses that improve the strength of an assembly. Compared to prior work, our approach is more generally applicable than commonly used heuristics and more efficient than dynamics simulations.

In this paper, we propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms by modeling them as first-order integro-differential equations. We perform numerical simulations of these equations to demonstrate their validity as accurate approximations of the original algorithms. Our results indicate a strong agreement between the behavior of the continuous-time models and the discrete implementations, thus providing a new perspective on the theoretical understanding of adaptive optimization methods. The pursuit of finding the global minima of such functions presents a significant challenge due to the inherent complexity and non-convexity of the landscape. Gradient Descent (GD) remains one of the most prominent algorithms for minimizing the function f by iteratively finding the optimal parameters θ Boyd & Vandenberghe (2004). It operates by adjusting the parameters in the direction of the steepest descent of f with a fixed step size α (learning rate). At each iteration, the algorithm computes the gradient of f with respect to θ, guiding the parameter updates to minimize f progressively Rumelhart et al. (1986): θ The continuous nature of these methods permits a more direct application of differential equation techniques. For readers interested in a continuous description of the stochastic method, we refer to Sirignano & Spiliopoulos (2017). Adaptive optimization methods such as AdaGrad Duchi et al. (2011) and RMSProp Hinton (2012) have been pivotal in advancing gradient-based algorithms.

The rapid advancement of low Earth orbit (LEO) satellite communication systems has significantly enhanced global connectivity, offering high-capacity, low-latency services crucial for next-generation applications. However, the dense configuration of LEO constellations poses challenges in resource allocation optimization and interference management, complicating coexistence with other communication systems. To address these limitations, this paper proposes a novel framework for optimizing the beam scheduling and resource allocation in multi-beam LEO systems. To satisfy the uneven terrestrial traffic demand, a hybrid beam pattern is employed to enhance the downlink quality of service and minimize the transmission latency from LEO satellites to ground user terminals. Additionally, a dynamic co-channel interference (CCI) control mechanism is developed to mitigate inter-beam interference within the LEO constellation and limit cross-system interference affecting protected users from other networks. The problem of user-beam-frequency allocation with power optimization is formulated as a mixed-integer dynamic programming model and solved using a low-complexity neural network-based graph generation algorithm. Simulation results show that the proposed approach outperforms the baseline methods of full frequency reuse and single-channel transmission, and highlights the potential for further performance improvement with multi-user transmissions.

Natural language allows robot programming to be accessible to everyone. However, the inherent fuzziness in natural language poses challenges for inflexible, traditional robot systems. We focus on instructions with fuzzy time requirements (e.g., "start in a few minutes"). Building on previous robotics research, we introduce fuzzy skills. These define an execution by the robot with so-called satisfaction functions representing vague execution time requirements. Such functions express a user's satisfaction over potential starting times for skill execution. When the robot handles multiple fuzzy skills, the satisfaction function provides a temporal tolerance window for execution, thus, enabling optimal scheduling based on satisfaction. We generalized such functions based on individual user expectations with a user study. The participants rated their satisfaction with an instruction's execution at various times. Our investigations reveal that trapezoidal functions best approximate the users' satisfaction. Additionally, the results suggest that users are more lenient if the execution is specified further into the future.

Minimax optimization is gaining increasing attention in modern machine learning applications. Driven by large-scale models and massive volumes of data collected from edge devices, as well as the concern to preserve client privacy, communication-efficient distributed minimax optimization algorithms become popular, such as Local Stochastic Gradient Descent Ascent (Local-SGDA), and Local Decentralized SGDA (Local-DSGDA). While most existing research on distributed minimax algorithms focuses on convergence rates, computation complexity, and communication efficiency, the generalization performance remains underdeveloped, whereas generalization ability is a pivotal indicator for evaluating the holistic performance of a model when fed with unknown data. In this paper, we propose the stability-based generalization analytical framework for Distributed-SGDA, which unifies two popular distributed minimax algorithms including Local-SGDA and Local-DSGDA, and conduct a comprehensive analysis of stability error, generalization gap, and population risk across different metrics under various settings, e.g., (S)C-(S)C, PL-SC, and NC-NC cases. Our theoretical results reveal the trade-off between the generalization gap and optimization error and suggest hyperparameters choice to obtain the optimal population risk.

Machine learning models deployed on edge devices have enabled numerous exciting new applications, such as humanoid robots, AR glasses, and autonomous vehicles. However, the computing resources available on these edge devices are not catching up with the ever-growing number of parameters in these models. As the models become bigger and more complicated, the novel yet sophisticated structure challenges the inference runtime optimization. ML, a generic runtime memory management and optimization framework that can flexibly transform the model execution blueprint to achieve faster and more memory-efficient inference. ML can consistently reduce the end-to-end inference latency by up to 25.38% for popular language models and reduce peak memory usage by up to 41.47%, compared to state-of-the-art approaches. ML is of 30K line of codes, built for general-purpose usage, and will be released as an open-source inference runtime optimization framework to the community. Fundamentally, there is a lack of a generic, Taking advantage of near-sensor inference, machine learning model-agnostic framework that can provide a holistic plan (ML) models deployed on edge devices enabled many for how the numeric computation should flow throughout low-latency, low-power, and privacy-sensitive applications.

The Travelling Salesman Problem (TSP) remains a fundamental challenge in combinatorial optimization, inspiring diverse algorithmic strategies. This paper revisits the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm that has recently gained traction for learning-based TSP solutions. Within this framework, heatmaps encode the likelihood of edges forming part of the optimal tour, and MCTS refines this probabilistic guidance to discover optimal solutions. Contemporary approaches have predominantly emphasized the refinement of heatmap generation through sophisticated learning models, inadvertently sidelining the critical role of MCTS. Our extensive empirical analysis reveals two pivotal insights: 1) The configuration of MCTS strategies profoundly influences the solution quality, demanding meticulous tuning to leverage their full potential; 2) Our findings demonstrate that a rudimentary and parameter-free heatmap, derived from the intrinsic k-nearest nature of TSP, can rival or even surpass the performance of complicated heatmaps, with strong generalizability across various scales. Empirical evaluations across various TSP scales underscore the efficacy of our approach, achieving competitive results. These observations challenge the prevailing focus on heatmap sophistication, advocating a reevaluation of the paradigm to harness both components synergistically. The Travelling Salesman Problem (TSP) stands as a quintessential challenge in combinatorial optimization, drawing considerable interest from both theoretical and applied research communities. As a problem characterized by NP-hardness, the TSP has become a benchmark for evaluating the efficacy of novel algorithmic strategies in determining optimal or near-optimal solutions efficiently (Applegate et al., 2009). It has significant practical applications in domains such as logistics, transportation, manufacturing, and telecommunications, where finding efficient routes is crucial for minimizing costs and improving efficiency (Helsgaun, 2017; Nagata & Kobayashi, 2013). Recent advancements in machine learning have inspired a fresh wave of methodologies for tackling the TSP, particularly through the lens of the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm.

Designing planners and controllers for contact-rich manipulation is extremely challenging as contact violates the smoothness conditions that many gradient-based controller synthesis tools assume. Contact smoothing approximates a non-smooth system with a smooth one, allowing one to use these synthesis tools more effectively. However, applying classical control synthesis methods to smoothed contact dynamics remains relatively under-explored. This paper analyzes the efficacy of linear controller synthesis using differential simulators based on contact smoothing. We introduce natural baselines for leveraging contact smoothing to compute (a) open-loop plans robust to uncertain conditions and/or dynamics, and (b) feedback gains to stabilize around open-loop plans. Using robotic bimanual whole-body manipulation as a testbed, we perform extensive empirical experiments on over 300 trajectories and analyze why LQR seems insufficient for stabilizing contact-rich plans. The video summarizing this paper and hardware experiments is found here: https://youtu.be/HLaKi6qbwQg?si=_zCAmBBD6rGSitm9.