For each sequence we plot the reference solution and enumerate metadata including - The sequence name, source data, component trials, total duration (MM:SS), total distance traveled, and the number (#) of measurements plus outlier rate (%) for both intra-robot (LC) and inter-robot (IRLC) loop-closures (#, %). For each sequence we generate a dataset using both the Wi-Fi and Pro-Radio communication model for a total of 24 datasets. Component trial names are shortened for brevity - "D" for "Day" and "N" for "Night" for the MCD data and "K" for "Kittredge Loop" and "M" for "Main Campus" for the CU-Multi data. Note: Plots are not to scale. Abstract -- Recent years have seen a focus on research into distributed optimization algorithms for multi-robot Collaborative Simultaneous Localization and Mapping (C-SLAM). Research in this domain, however, is made difficult by a lack of standard benchmark datasets. Such datasets have been used to great effect in the field of single-robot SLAM, and researchers focused on multi-robot problems would benefit greatly from dedicated benchmark datasets. T o address this gap, we design and release the C ollaborative O pen-Source M ulti-robot O ptimization Benchmark (COSMO-Bench) - a suite of 24 datasets derived from a baseline C-SLAM front-end and real-world LiDAR data.

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by a finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months, and is a significant cost in practice. We have developed a Bayesian optimization system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing a generalized inverse of a high-dimensional non-linear function that does not require e.g. gradient information, which is often unavailable from discipline models. We furthermore develop a two-tier convergence criterion based on (i) convergence to a solution optimally satisfying all specified design criteria, or (ii) convergence to a minimum-norm solution. We demonstrate the proposed approach on a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient, and that the novel convergence criteria can be implemented straightforwardly based on existing concepts and subroutines in popular Bayesian optimization software packages.

Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial dictionaries. Data-agnostic analytical dictionaries, such as the discrete Fourier transform, wavelets and graph Fourier, have seen wide adoption due to efficient implementations and good practical performance. On the other hand, dictionaries learned from data offer sparser and more accurate solutions but require learning of both the dictionaries and the coding coefficients. This becomes especially challenging for multi-dictionary scenarios since encoding coefficients correspond to all atom combinations from the dictionaries. To address this challenge, we propose a low-rank coding model for 2-dictionary scenarios and study its data complexity. Namely, we establish a bound on the number of samples needed to learn dictionaries that generalize to unseen samples from the same distribution. We propose a convex relaxation solution, called AODL, whose exact solution we show also solves the original problem. We then solve this relaxation via alternating optimization between the sparse coding matrices and the learned dictionaries, which we prove to be convergent. We demonstrate its quality for data reconstruction and missing value imputation in both synthetic and real-world datasets. For a fixed reconstruction quality, AODL learns up to 90\% sparser solutions compared to non-low-rank and analytical (fixed) dictionary baselines. In addition, the learned dictionaries reveal interpretable insights into patterns present within the samples used for training.

Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in such settings but methods like Local Stochastic Gradient Descent (Local SGD) show great promise in reducing this additional communication overhead. Local SGD consists of three parts: a local optimization process, an aggregation mechanism, and an outer optimizer that uses the aggregated updates from the nodes to produce a new model. While there exists an extensive literature on understanding the impact of hyperparameters in the local optimization process, the choice of outer optimizer and its hyperparameters is less clear. We study the role of the outer optimizer in Local SGD, and prove new convergence guarantees for the algorithm. In particular, we show that tuning the outer learning rate allows us to (a) trade off between optimization error and stochastic gradient noise variance, and (b) make up for ill-tuning of the inner learning rate. Our theory suggests that the outer learning rate should sometimes be set to values greater than $1$. We extend our results to settings where we use momentum in the outer optimizer, and we show a similar role for the momentum-adjusted outer learning rate. We also study acceleration in the outer optimizer and show that it improves the convergence rate as a function of the number of communication rounds, improving upon the convergence rate of prior algorithms that apply acceleration locally. Finally, we also introduce a novel data-dependent analysis of Local SGD that yields further insights on outer learning rate tuning. We conduct comprehensive experiments with standard language models and various outer optimizers to validate our theory.

Ensemble learning has been widely recognized as a pivotal technique for boosting predictive performance by combining multiple base models. Nevertheless, conventional margin-based ensemble methods predominantly focus on maximizing the expected margin while neglecting the critical role of margin variance, which inherently restricts the generalization capability of the model and heightens its vulnerability to overfitting, particularly in noisy or imbalanced datasets. Additionally, the conventional approach of optimizing ensemble weights within the probability simplex often introduces computational inefficiency and scalability challenges, complicating its application to large-scale problems. To tackle these limitations, this paper introduces a novel ensemble learning framework that explicitly incorporates margin variance into the loss function. Our method jointly optimizes the negative expected margin and its variance, leading to enhanced robustness and improved generalization performance. Moreover, by reparameterizing the ensemble weights onto the unit sphere, we substantially simplify the optimization process and improve computational efficiency. Extensive experiments conducted on multiple benchmark datasets demonstrate that the proposed approach consistently outperforms traditional margin-based ensemble techniques, underscoring its effectiveness and practical utility.

In the combinatorial semi-bandit (CSB) problem, a player selects an action from a combinatorial action set and observes feedback from the base arms included in the action. While CSB is widely applicable to combinatorial optimization problems, its restriction to binary decision spaces excludes important cases involving non-negative integer flows or allocations, such as the optimal transport and knapsack problems.To overcome this limitation, we propose the multi-play combinatorial semi-bandit (MP-CSB), where a player can select a non-negative integer action and observe multiple feedbacks from a single arm in each round. We propose two algorithms for the MP-CSB. One is a Thompson-sampling-based algorithm that is computationally feasible even when the action space is exponentially large with respect to the number of arms, and attains $O(\log T)$ distribution-dependent regret in the stochastic regime, where $T$ is the time horizon. The other is a best-of-both-worlds algorithm, which achieves $O(\log T)$ variance-dependent regret in the stochastic regime and the worst-case $\tilde{\mathcal{O}}\left( \sqrt{T} \right)$ regret in the adversarial regime. Moreover, its regret in adversarial one is data-dependent, adapting to the cumulative loss of the optimal action, the total quadratic variation, and the path-length of the loss sequence. Finally, we numerically show that the proposed algorithms outperform existing methods in the CSB literature.

Value-based approaches such as DQN are the default methods for off-policy reinforcement learning with discrete-action environments such as Atari. Common policy-based methods are either on-policy and do not effectively learn from off-policy data (e.g. PPO), or have poor empirical performance in the discrete-action setting (e.g. SAC). Consequently, starting from discrete SAC (DSAC), we revisit the design of actor-critic methods in this setting. First, we determine that the coupling between the actor and critic entropy is the primary reason behind the poor performance of DSAC. We demonstrate that by merely decoupling these components, DSAC can have comparable performance as DQN. Motivated by this insight, we introduce a flexible off-policy actor-critic framework that subsumes DSAC as a special case. Our framework allows using an m-step Bellman operator for the critic update, and enables combining standard policy optimization methods with entropy regularization to instantiate the resulting actor objective. Theoretically, we prove that the proposed methods can guarantee convergence to the optimal regularized value function in the tabular setting. Empirically, we demonstrate that these methods can approach the performance of DQN on standard Atari games, and do so even without entropy regularization or explicit exploration.

B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. Current methods rely on pre-computed kinematics databases generated through sampling to search for solutions. However, they face an inherent trade-off between solution optimality and computational efficiency when determining sampling resolution. To address these limitations, B* unifies multiple objectives without database dependence. The framework employs a two-layer hierarchical approach. The outer layer systematically manages terminal constraints through progressive tightening, particularly for base mobility, enabling feasible initialization and broad solution exploration. The inner layer addresses non-convexities in each outer-layer subproblem through sequential local linearization, converting the original problem into tractable sequential linear programming (SLP). Testing across multiple robot platforms demonstrates B*'s effectiveness. The framework achieves solution optimality five orders of magnitude better than sampling-based approaches while maintaining perfect success rates and reduced computational overhead. Operating directly in configuration space, B* enables simultaneous path planning with customizable optimization criteria. B* serves as a crucial initialization tool that bridges the gap between theoretical motion planning and practical deployment, where feasible trajectory existence is fundamental.

Federated learning (FL) offers an innovative paradigm for collaborative model training across decentralized devices, such as smartphones, balancing enhanced predictive performance with the protection of user privacy in sensitive areas like Internet of Things (IoT) and medical data analysis. Despite its advantages, FL encounters significant challenges related to user privacy protection against potential attacks and the management of communication costs. This paper introduces a novel federated learning algorithm called FedRP, which integrates random projection techniques with the Alternating Direction Method of Multipliers (ADMM) optimization framework. This approach enhances privacy by employing random projection to reduce the dimensionality of model parameters prior to their transmission to a central server, reducing the communication cost. The proposed algorithm offers a strong $(ε, δ)$-differential privacy guarantee, demonstrating resilience against data reconstruction attacks. Experimental results reveal that FedRP not only maintains high model accuracy but also outperforms existing methods, including conventional differential privacy approaches and FedADMM, in terms of both privacy preservation and communication efficiency.

Mechanical compliance is a key design parameter for dynamic contact-rich manipulation, affecting task success and safety robustness over contact geometry variation. Design of soft robotic structures, such as compliant fingers, requires choosing design parameters which affect geometry and stiffness, and therefore manipulation performance and robustness. Today, these parameters are chosen through either hardware iteration, which takes significant development time, or simplified models (e.g. planar), which can't address complex manipulation task objectives. Improvements in dynamic simulation, especially with contact and friction modeling, present a potential design tool for mechanical compliance. We propose a simulation-based design tool for compliant mechanisms which allows design with respect to task-level objectives, such as success rate. This is applied to optimize design parameters of a structured compliant finger to reduce failure cases inside a tolerance window in insertion tasks. The improvement in robustness is then validated on a real robot using tasks from the benchmark NIST task board. The finger stiffness affects the tolerance window: optimized parameters can increase tolerable ranges by a factor of 2.29, with workpiece variation up to 8.6 mm being compensated. However, the trends remain task-specific. In some tasks, the highest stiffness yields the widest tolerable range, whereas in others the opposite is observed, motivating need for design tools which can consider application-specific geometry and dynamics.