The impact of inference-time data perturbation (e.g., adversarial attacks) has been extensively studied in machine learning, leading to well-established certification techniques for adversarial robustness. In contrast, certifying models against training data perturbations remains a relatively under-explored area. These perturbations can arise in three critical contexts: adversarial data poisoning, where an adversary manipulates training samples to corrupt model performance; machine unlearning, which requires certifying model behavior under the removal of specific training data; and differential privacy, where guarantees must be given with respect to substituting individual data points. This work introduces Abstract Gradient Training (AGT), a unified framework for certifying robustness of a given model and training procedure to training data perturbations, including bounded perturbations, the removal of data points, and the addition of new samples. By bounding the reachable set of parameters, i.e., establishing provable parameter-space bounds, AGT provides a formal approach to analyzing the behavior of models trained via first-order optimization methods.

We consider the problem of certified robustness for sequence classification against edit distance perturbations. Naturally occurring inputs of varying lengths (e.g., sentences in natural language processing tasks) present a challenge to current methods that employ fixed-rate deletion mechanisms and lead to suboptimal performance. To this end, we introduce AdaptDel methods with adaptable deletion rates that dynamically adjust based on input properties. We extend the theoretical framework of randomized smoothing to variable-rate deletion, ensuring sound certification with respect to edit distance. We achieve strong empirical results in natural language tasks, observing up to 30 orders of magnitude improvement to median cardinality of the certified region, over state-of-the-art certifications.

In recent years, graph neural networks (GNNs) have been widely applied in tackling combinatorial optimization problems. However, existing methods still suffer from limited accuracy when addressing that on complex graphs and exhibit poor scalability, since full training requires loading the whole adjacent matrix and all embeddings at a time, the it may results in out of memory of a single machine. This limitation significantly restricts their applicability to large-scale scenarios. To address these challenges, we propose a distributed GNN-based training framework for combinatorial optimization. In details, firstly, large graph is partition into several small subgraphs. Then the individual subgraphs are full trained, providing a foundation for efficient local optimization. Finally, reinforcement learning (RL) are employed to take actions according to GNN output, to make sure the restrictions between cross nodes can be learned. Extensive experiments are conducted on both real large-scale social network datasets (e.g., Facebook, Youtube) and synthetically generated high-complexity graphs, which demonstrate that our framework outperforms state-of-the-art approaches in both solution quality and computational efficiency. Moreover, the experiments on large graph instances also validate the scalability of the model.

Hyperparameter Optimization (HPO) can lift the burden of tuning hyperparameters (HPs) of neural networks. HPO algorithms from the Population Based Training (PBT) family are efficient thanks to dynamically adjusting HPs every few steps of the weight optimization. Recent results indicate that the number of steps between HP updates is an important meta-HP of all PBT variants that can substantially affect their performance. Yet, no method or intuition is available for efficiently setting its value. We introduce Iterated Population Based Training (IPBT), a novel PBT variant that automatically adjusts this HP via restarts that reuse weight information in a task-agnostic way and leverage time-varying Bayesian optimization to reinitialize HPs. Evaluation on 8 image classification and reinforcement learning tasks shows that, on average, our algorithm matches or outperforms 5 previous PBT variants and other HPO algorithms (random search, ASHA, SMAC3), without requiring a budget increase or any changes to its HPs. The source code is available at https://github.com/AwesomeLemon/IPBT.

LiDAR-inertial odometry (LIO) has been widely used in robotics due to its high accuracy. However, its performance degrades in degenerate environments, such as long corridors and high-altitude flights, where LiDAR measurements are imbalanced or sparse, leading to ill-posed state estimation. In this letter, we present LODESTAR, a novel LIO method that addresses these degeneracies through two key modules: degeneracy-aware adaptive Schmidt-Kalman filter (DA-ASKF) and degeneracy-aware data exploitation (DA-DE). DA-ASKF employs a sliding window to utilize past states and measurements as additional constraints. Specifically, it introduces degeneracy-aware sliding modes that adaptively classify states as active or fixed based on their degeneracy level. Using Schmidt-Kalman update, it partially optimizes active states while preserving fixed states. These fixed states influence the update of active states via their covariances, serving as reference anchors--akin to a lodestar. Additionally, DA-DE prunes less-informative measurements from active states and selectively exploits measurements from fixed states, based on their localizability contribution and the condition number of the Jacobian matrix. Consequently, DA-ASKF enables degeneracy-aware constrained optimization and mitigates measurement sparsity, while DA-DE addresses measurement imbalance. Experimental results show that LODESTAR outperforms existing LiDAR-based odometry methods and degeneracy-aware modules in terms of accuracy and robustness under various degenerate conditions.

We propose Federated Preconditioned Mixing (FedPM), a novel Federated Learning (FL) method that leverages second-order optimization. Prior methods--such as LocalNewton, LTDA, and FedSophia--have incorporated second-order optimization in FL by performing iterative local updates on clients and applying simple mixing of local parameters on the server. However, these methods often suffer from drift in local preconditioners, which significantly disrupts the convergence of parameter training, particularly in heterogeneous data settings. To overcome this issue, we refine the update rules by decomposing the ideal second-order update--computed using globally preconditioned global gradients--into parameter mixing on the server and local parameter updates on clients. As a result, our FedPM introduces preconditioned mixing of local parameters on the server, effectively mitigating drift in local preconditioners. We provide a theoretical convergence analysis demonstrating a superlinear rate for strongly convex objectives in scenarios involving a single local update. To demonstrate the practical benefits of FedPM, we conducted extensive experiments. The results showed significant improvements with FedPM in the test accuracy compared to conventional methods incorporating simple mixing, fully leveraging the potential of second-order optimization.

Optimization modeling and solving are fundamental to the application of Operations Research (OR) in real-world decision making, yet the process of translating natural language problem descriptions into formal models and solver code remains highly expertise intensive. While recent advances in large language models (LLMs) have opened new opportunities for automation, the generalization ability and data efficiency of existing LLM-based methods are still limited, asmost require vast amounts of annotated or synthetic data, resulting in high costs and scalability barriers. In this work, we present OR-R1, a data-efficient training framework for automated optimization modeling and solving. OR-R1 first employs supervised fine-tuning (SFT) to help the model acquire the essential reasoning patterns for problem formulation and code generation from limited labeled data. In addition, it improves the capability and consistency through Test-Time Group Relative Policy Optimization (TGRPO). This two-stage design enables OR-R1 to leverage both scarce labeled and abundant unlabeled data for effective learning. Experiments show that OR-R1 achieves state-of-the-art performance with an average solving accuracy of $67.7\%$, using only $1/10$ the synthetic data required by prior methods such as ORLM, exceeding ORLM's solving accuracy by up to $4.2\%$. Remarkably, OR-R1 outperforms ORLM by over $2.4\%$ with just $100$ synthetic samples. Furthermore, TGRPO contributes an additional $3.1\%-6.4\%$ improvement in accuracy, significantly narrowing the gap between single-attempt (Pass@1) and multi-attempt (Pass@8) performance from $13\%$ to $7\%$. Extensive evaluations across diverse real-world benchmarks demonstrate that OR-R1 provides a robust, scalable, and cost-effective solution for automated OR optimization problem modeling and solving, lowering the expertise and data barriers for industrial OR applications.

Interactive preference elicitation (IPE) aims to substantially reduce human effort while acquiring human preferences in wide personalization systems. Dueling bandit (DB) algorithms enable optimal decision-making in IPE building on pairwise comparisons. However, they remain inefficient when human feedback is sparse. Existing methods address sparsity by heavily relying on parametric reward models, whose rigid assumptions are vulnerable to misspecification. In contrast, we explore an alternative perspective based on feedback augmentation, and introduce critical improvements to the model-free DB framework. Specifically, we introduce augmented confidence bounds to integrate augmented human feedback under generalized concentration properties, and analyze the multi-factored performance trade-off via regret analysis. Our prototype algorithm achieves competitive performance across several IPE benchmarks, including recommendation, multi-objective optimization, and response optimization for large language models, demonstrating the potential of our approach for provably efficient IPE in broader applications.

With the widespread adoption of unmanned aerial vehicles (UAV), effective path planning has become increasingly important. Although traditional search methods have been extensively applied, metaheuristic algorithms have gained popularity due to their efficiency and problem-specific heuristics. However, challenges such as premature convergence and lack of solution diversity still hinder their performance in complex scenarios. To address these issues, this paper proposes an Enhanced Multi-Strategy Dwarf Mongoose Optimization (EDMO) algorithm, tailored for three-dimensional UAV trajectory planning in dynamic and obstacle-rich environments. EDMO integrates three novel strategies: (1) a Dynamic Quantum Tunneling Optimization Strategy (DQTOS) to enable particles to probabilistically escape local optima; (2) a Bio-phototactic Dynamic Focusing Search Strategy (BDFSS) inspired by microbial phototaxis for adaptive local refinement; and (3) an Orthogonal Lens Opposition-Based Learning (OLOBL) strategy to enhance global exploration through structured dimensional recombination. EDMO is benchmarked on 39 standard test functions from CEC2017 and CEC2020, outperforming 14 advanced algorithms in convergence speed, robustness, and optimization accuracy. Furthermore, real-world validations on UAV three-dimensional path planning and three engineering design tasks confirm its practical applicability and effectiveness in field robotics missions requiring intelligent, adaptive, and time-efficient planning.

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.