V alue iteration (VI) [4] is the practically most used method for reliable analysis of probabilistic systems, in particular Markov decision processes (MDPs) [21] and stochastic games (SGs) [8]. It is used in the state-of-the-art model checkers such as Prism [18] and Storm [11] as the default method due to its better practical scalability, compared to strategy iteration or linear/quadratic programming [14, 19]. The price to pay are issues with precision. Firstly, while other methods yield precise results in theory (omitting floating-point issues), VI converges to the exact result only in the limit. Secondly, the precision of the intermediate iterations was until recently an open question. Given the importance of reliable precision in verification, many recent works focused on modifying VI so that the imprecision can be bounded, yielding a stopping criterion. Consequently, (i) the computed result is reliable, and (ii) the procedure can even terminate earlier whenever the desired precision is achieved.

Abstract--Wheel-legged robots with integrated manipulators hold great promise for mobile manipulation in logistics, industrial automation, and human-robot collaboration. However, unified control of such systems remains challenging due to the redundancy in degrees of freedom, complex wheel-ground contact dynamics, and the need for seamless coordination between locomotion and manipulation. In this work, we present the design and whole-body motion control of an omnidirectional wheel-legged quadrupedal robot equipped with a dexterous manipulator . The proposed platform incorporates independently actuated steering modules and hub-driven wheels, enabling agile omnidirectional locomotion with high maneuverability in structured environments. T o address the challenges of contact-rich interaction, we develop a contact-aware whole-body dynamic optimization framework that integrates point-contact modeling for manipulation with line-contact modeling for wheel-ground interactions. A warm-start strategy is introduced to accelerate online optimization, ensuring real-time feasibility for high-dimensional control. Furthermore, a unified kinematic model tailored for the robot's 4WIS-4WID actuation scheme eliminates the need for mode switching across different locomotion strategies, improving control consistency and robustness. Simulation and experimental results validate the effectiveness of the proposed framework, demonstrating agile terrain traversal, high-speed omnidirectional mobility, and precise manipulation under diverse scenarios, underscoring the system's potential for factory automation, urban logistics, and service robotics in semi-structured environments. HEEL-LEGGED quadrupedal robots have demonstrated strong potential for applications such as material transport in factories and indoor-outdoor logistics, owing to their superior mobility and terrain adaptability. By integrating a dexterous manipulator, such robots are further equipped with autonomous manipulation capabilities, enabling tasks such as grasping, handling, sorting, and delivery (see Figure 1).

Non-IID data and partial participation induce client drift and inconsistent local optima in federated learning, causing unstable convergence and accuracy loss. We present FedSSG, a stochastic sampling-guided, history-aware drift alignment method. FedSSG maintains a per-client drift memory that accumulates local model differences as a lightweight sketch of historical gradients; crucially, it gates both the memory update and the local alignment term by a smooth function of the observed/expected participation ratio (a phase-by-expectation signal derived from the server sampler). This statistically grounded gate stays weak and smooth when sampling noise dominates early, then strengthens once participation statistics stabilize, contracting the local-global gap without extra communication. Across CIFAR-10/100 with 100/500 clients and 2-15 percent participation, FedSSG consistently outperforms strong drift-aware baselines and accelerates convergence; on our benchmarks it improves test accuracy by up to a few points (e.g., about +0.9 on CIFAR-10 and about +2.7 on CIFAR-100 on average over the top-2 baseline) and yields about 4.5x faster target-accuracy convergence on average. The method adds only O(d) client memory and a constant-time gate, and degrades gracefully to a mild regularizer under near-IID or uniform sampling. FedSSG shows that sampling statistics can be turned into a principled, history-aware phase control to stabilize and speed up federated training.

Regret minimization is a powerful method for finding Nash equilibria in Normal-Form Games (NFGs) and Extensive-Form Games (EFGs), but it typically guarantees convergence only for the average strategy. However, computing the average strategy requires significant computational resources or introduces additional errors, limiting its practical applicability. The Reward Transformation (RT) framework was introduced to regret minimization to achieve last-iterate convergence through reward function regularization. However, it faces practical challenges: its performance is highly sensitive to manually tuned parameters, which often deviate from theoretical convergence conditions, leading to slow convergence, oscillations, or stagnation in local optima. Inspired by previous work, we propose an adaptive technique to address these issues, ensuring better consistency between theoretical guarantees and practical performance for RT Regret Matching (RTRM), RT Counterfactual Regret Minimization (RTCFR), and their variants in solving NFGs and EFGs more effectively. Our adaptive methods dynamically adjust parameters, balancing exploration and exploitation while improving regret accumulation, ultimately enhancing asymptotic last-iterate convergence and achieving linear convergence. Experimental results demonstrate that our methods significantly accelerate convergence, outperforming state-of-the-art algorithms.

The fairness-accuracy trade-off is a key challenge in NLP tasks. Current work focuses on finding a single "optimal" solution to balance the two objectives, which is limited considering the diverse solutions on the Pareto front. This work intends to provide controllable trade-offs according to the user's preference of the two objectives, which is defined as a reference vector. To achieve this goal, we apply multi-objective optimization (MOO), which can find solutions from various regions of the Pareto front. However, it is challenging to precisely control the trade-off due to the stochasticity of the training process and the high dimentional gradient vectors. Thus, we propose Controllable Pareto Trade-off (CPT) that can effectively train models to perform different trade-offs according to users' preferences. CPT 1) stabilizes the fairness update with a moving average of stochastic gradients to determine the update direction, and 2) prunes the gradients by only keeping the gradients of the critical parameters. We evaluate CPT on hate speech detection and occupation classification tasks. Experiments show that CPT can achieve a higher-quality set of solutions on the Pareto front than the baseline methods. It also exhibits better controllability and can precisely follow the human-defined reference vectors.

Abstract--Federated learning (FL) has gained popularity as a privacy-preserving method of training machine learning models on decentralized networks. However to ensure reliable operation of UA V-assisted FL systems, issues like as excessive energy consumption, communication inefficiencies, and security vulnerabilities must be solved. This paper proposes an innovative framework that integrates Digital Twin (DT) technology and Zero-Knowledge Federated Learning (zkFed) to tackle these challenges. UA Vs act as mobile base stations, allowing scattered devices to train FL models locally and upload model updates for aggregation. By incorporating DT technology, our approach enables real-time system monitoring and predictive maintenance, improving UA V network efficiency. Additionally, Zero-Knowledge Proofs (ZKPs) strengthen security by allowing model verification without exposing sensitive data. T o optimize energy efficiency and resource management, we introduce a dynamic allocation strategy that adjusts UA V flight paths, transmission power, and processing rates based on network conditions. Using block coordinate descent and convex optimization techniques, our method significantly reduces system energy consumption by up to 29.6% compared to conventional FL approaches. Simulation results demonstrate improved learning performance, security, and scalability, positioning this framework as a promising solution for next-generation UA V-based intelligent networks. Federated learning (FL) is transforming how machine learning models are trained in distributed networks. Instead of collecting and processing data at a central server, FL allows devices to train models locally and share only the learned parameters. This decentralized approach helps protect user privacy, reduce communication overhead, and improve scalability [1], [2].

We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. The progress metric is the Pareto stationarity gap $\mathcal{G}(x)$ (the norm of an optimal convex combination of gradients). Our contributions are fourfold. (i) For strongly convex objectives, any span first-order method (iterates lie in the span of past gradients) exhibits linear convergence no faster than $\exp(-Θ(T/\sqrtκ))$ after $T$ oracle calls, where $κ$ is the condition number, implying $Θ(\sqrtκ\log(1/\varepsilon))$ iterations; this matches classical accelerated upper bounds. (ii) For convex problems and oblivious one-step methods (a fixed scalarization with pre-scheduled step sizes), we prove a lower bound of order $1/T$ on the best gradient norm among the first $T$ iterates. (iii) Although accelerated gradient descent is outside this restricted class, it is an oblivious span method and attains the same $1/T$ upper rate on a fixed scalarization. (iv) For convex problems and general span methods with adaptive scalarizations, we establish a universal lower bound of order $1/T^{2}$ on the gradient norm of the final iterate after $T$ steps, highlighting a gap between known upper bounds and worst-case guarantees. All bounds hold on non-degenerate instances with distinct objectives and non-singleton Pareto fronts; rates are stated up to universal constants and natural problem scaling.

Bio-inspired algorithms utilize natural processes such as evolution, swarm behavior, foraging, and plant growth to solve complex, nonlinear, high-dimensional optimization problems. However, a plethora of these algorithms require a more rigorous review before making them applicable to the relevant fields. This survey categorizes these algorithms into eight groups: evolutionary, swarm intelligence, physics-inspired, ecosystem and plant-based, predator-prey, neural-inspired, human-inspired, and hybrid approaches, and reviews their principles, strengths, novelty, and critical limitations. We provide a critique on the novelty issues of many of these algorithms. We illustrate some of the suitable usage of the prominent algorithms in machine learning, engineering design, bioinformatics, and intelligent systems, and highlight recent advances in hybridization, parameter tuning, and adaptive strategies. Finally, we identify open challenges such as scalability, convergence, reliability, and interpretability to suggest directions for future research. This work aims to serve as a resource for both researchers and practitioners interested in understanding the current landscape and future directions of reliable and authentic advancement of bio-inspired algorithms.

Although robotic manipulators are used in an ever-growing range of applications, robot manufacturers typically follow a ``one-fits-all'' philosophy, employing identical manipulators in various settings. This often leads to suboptimal performance, as general-purpose designs fail to exploit particularities of tasks. The development of custom, task-tailored robots is hindered by long, cost-intensive development cycles and the high cost of customized hardware. Recently, various computational design methods have been devised to overcome the bottleneck of human engineering. In addition, a surge of modular robots allows quick and economical adaptation to changing industrial settings. This work proposes an approach to automatically designing and optimizing robot morphologies tailored to a specific environment. To this end, we learn the inverse kinematics for a wide range of different manipulators. A fully differentiable framework realizes gradient-based fine-tuning of designed robots and inverse kinematics solutions. Our generative approach accelerates the generation of specialized designs from hours with optimization-based methods to seconds, serving as a design co-pilot that enables instant adaptation and effective human-AI collaboration. Numerical experiments show that our approach finds robots that can navigate cluttered environments, manipulators that perform well across a specified workspace, and can be adapted to different hardware constraints. Finally, we demonstrate the real-world applicability of our method by setting up a modular robot designed in simulation that successfully moves through an obstacle course.

Despite the widespread deployment of terrestrial networks, providing reliable communication services to remote areas and maintaining connectivity during emergencies remains challenging. Low Earth orbit (LEO) satellite constellations offer promising solutions with their global coverage capabilities and reduced latency, yet struggle with intermittent coverage and limited communication windows due to orbital dynamics. This paper introduces an age of information (AoI)-aware space-air-ground integrated network (SAGIN) architecture that leverages a high-altitude platform (HAP) as intelligent relay between the LEO satellites and ground terminals. Our three-layer design employs hybrid free-space optical (FSO) links for high-capacity satellite-to-HAP communication and reliable radio frequency (RF) links for HAP-to-ground transmission, and thus addressing the temporal discontinuity in LEO satellite coverage while serving diverse user priorities. Specifically, we formulate a joint optimization problem to simultaneously minimize the AoI and satellite handover frequency through optimal transmit power distribution and satellite selection decisions. This highly dynamic, non-convex problem with time-coupled constraints presents significant computational challenges for traditional approaches. To address these difficulties, we propose a novel diffusion model (DM)-enhanced dueling double deep Q-network with action decomposition and state transformer encoder (DD3QN-AS) algorithm that incorporates transformer-based temporal feature extraction and employs a DM-based latent prompt generative module to refine state-action representations through conditional denoising. Simulation results highlight the superior performance of the proposed approach compared with policy-based methods and some other deep reinforcement learning (DRL) benchmarks.