Interpretable and explainable machine learning has seen a recent surge of interest.

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven empirical success in applications, the cumulative regret upper bound of EI remains an open question. In this paper, we analyze the classic noisy Gaussian process expected improvement (GP-EI) algorithm. We consider the Bayesian setting, where the objective is a sample from a GP. Three commonly used incumbents, namely the best posterior mean incumbent (BPMI), the best sampled posterior mean incumbent (BSPMI), and the best observation incumbent (BOI) are considered as the choices of the current best value in GP-EI. We present for the first time the cumulative regret upper bounds of GP-EI with BPMI and BSPMI. Importantly, we show that in both cases, GP-EI is a no-regret algorithm for both squared exponential (SE) and Matérn kernels. Further, we present for the first time that GP-EI with BOI either achieves a sublinear cumulative regret upper bound or has a fast converging noisy simple regret bound for SE and Matérn kernels. Our results provide theoretical guidance to the choice of incumbent when practitioners apply GP-EI in the noisy setting. Numerical experiments are conducted to validate our findings.

Large Language Models (LLMs) have made significant strides in reasoning tasks through methods like chain-of-thought (CoT) reasoning. However, they often fall short in tasks requiring precise computations. Tool-Integrated Reasoning (TIR) has emerged as a solution by incorporating external tools into the reasoning process. Nevertheless, the generalization of TIR in improving the reasoning ability of LLM is still unclear. Additionally, whether TIR has improved the model's reasoning behavior and helped the model think remains to be studied. We introduce ReasonZoo, a comprehensive benchmark encompassing nine diverse reasoning categories, to evaluate the effectiveness of TIR across various domains. Additionally, we propose two novel metrics, Performance-Aware Cost (PAC) and Area Under the Performance-Cost Curve (AUC-PCC), to assess reasoning efficiency. Our empirical evaluation demonstrates that TIR-enabled models consistently outperform their non-TIR counterparts in both mathematical and non-mathematical tasks. Furthermore, TIR enhances reasoning efficiency, as evidenced by improved PAC and AUC-PCC, indicating reduced overthinking and more streamlined reasoning. These findings underscore the domain-general benefits of TIR and its potential to advance LLM capabilities in complex reasoning tasks.

This study proposes a dynamic coupling-informed trajectory optimization algorithm for free-floating space manipulator systems (SMSs). Dynamic coupling between the base and the manipulator arms plays a critical role in influencing the system's behavior. While prior research has predominantly focused on minimizing this coupling, often overlooking its potential advantages, this work investigates how dynamic coupling can instead be leveraged to improve trajectory planning. Singular value decomposition (SVD) of the dynamic coupling matrix is employed to identify the dominant components governing coupling behavior. A quantitative metric is then formulated to characterize the strength and directionality of the coupling and is incorporated into a trajectory optimization framework. To assess the feasibility of the optimized trajectory, a sliding mode control-based tracking controller is designed to generate the required joint torque inputs. Simulation results demonstrate that explicitly accounting for dynamic coupling in trajectory planning enables more informed and potentially more efficient operation, offering new directions for the control of free-floating SMSs.

We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a wide range of first-order algorithms that can be expressed as an interconnection of a linear dynamical system in feedback with a first-order oracle. By leveraging Integral Quadratic Constraints (IQCs), we derive a semi-definite program which, when feasible, provides a regret guarantee for the online algorithm. For this, the concept of variational IQCs is introduced as the generalization of IQCs to time-varying monotone operators. Our bounds capture the temporal rate of change of the problem in the form of the path length of the time-varying minimizer and the objective function variation. In contrast to standard results in OCO, our results do not require nerither the assumption of gradient boundedness, nor that of a bounded feasible set. Numerical analyses showcase the ability of the approach to capture the dependence of the regret on the function class condition number.

Existing methods for concealed visual perception (CVP) often leverage reversible strategies to decrease uncertainty, yet these are typically confined to the mask domain, leaving the potential of the RGB domain underexplored. To address this, we propose a reversible unfolding network with generative refinement, termed RUN++. Specifically, RUN++ first formulates the CVP task as a mathematical optimization problem and unfolds the iterative solution into a multi-stage deep network. This approach provides a principled way to apply reversible modeling across both mask and RGB domains while leveraging a diffusion model to resolve the resulting uncertainty. Each stage of the network integrates three purpose-driven modules: a Concealed Object Region Extraction (CORE) module applies reversible modeling to the mask domain to identify core object regions; a Context-Aware Region Enhancement (CARE) module extends this principle to the RGB domain to foster better foreground-background separation; and a Finetuning Iteration via Noise-based Enhancement (FINE) module provides a final refinement. The FINE module introduces a targeted Bernoulli diffusion model that refines only the uncertain regions of the segmentation mask, harnessing the generative power of diffusion for fine-detail restoration without the prohibitive computational cost of a full-image process. This unique synergy, where the unfolding network provides a strong uncertainty prior for the diffusion model, allows RUN++ to efficiently direct its focus toward ambiguous areas, significantly mitigating false positives and negatives. Furthermore, we introduce a new paradigm for building robust CVP systems that remain effective under real-world degradations and extend this concept into a broader bi-level optimization framework.

Dexterous robotic hands enable versatile interactions due to the flexibility and adaptability of multi-fingered designs, allowing for a wide range of task-specific grasp configurations in diverse environments. However, to fully exploit the capabilities of dexterous hands, access to diverse and high-quality grasp data is essential -- whether for developing grasp prediction models from point clouds, training manipulation policies, or supporting high-level task planning with broader action options. Existing approaches for dataset generation typically rely on sampling-based algorithms or simplified force-closure analysis, which tend to converge to power grasps and often exhibit limited diversity. In this work, we propose a method to synthesize large-scale, diverse, and physically feasible grasps that extend beyond simple power grasps to include refined manipulations, such as pinches and tri-finger precision grasps. We introduce a rigorous, differentiable energy formulation of force closure, implicitly defined through a Quadratic Program (QP). Additionally, we present an adjusted optimization method (MALA*) that improves performance by dynamically rejecting gradient steps based on the distribution of energy values across all samples. We extensively evaluate our approach and demonstrate significant improvements in both grasp diversity and the stability of final grasp predictions. Finally, we provide a new, large-scale grasp dataset for 5,700 objects from DexGraspNet, comprising five different grippers and three distinct grasp types. Dataset and Code:https://graspqp.github.io/

Federated learning (FL) has emerged as a powerful paradigm for collaborative model training across distributed clients while preserving data privacy. However, existing FL algorithms predominantly focus on unconstrained optimization problems with exact gradient information, limiting its applicability in scenarios where only noisy function evaluations are accessible or where model parameters are constrained. To address these challenges, we propose a novel zeroth-order projection-based algorithm on Riemannian manifolds for FL. By leveraging the projection operator, we introduce a computationally efficient zeroth-order Riemannian gradient estimator. Unlike existing estimators, ours requires only a simple Euclidean random perturbation, eliminating the need to sample random vectors in the tangent space, thus reducing computational cost. Theoretically, we first prove the approximation properties of the estimator and then establish the sublinear convergence of the proposed algorithm, matching the rate of its first-order counterpart. Numerically, we first assess the efficiency of our estimator using kernel principal component analysis. Furthermore, we apply the proposed algorithm to two real-world scenarios: zeroth-order attacks on deep neural networks and low-rank neural network training to validate the theoretical findings.