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This paper presents an efficient preference elicitation framework for uncertain matroid optimization, where precise weight information is unavailable, but insights into possible weight values are accessible. The core innovation of our approach lies in its ability to systematically elicit user preferences, aligning the optimization process more closely with decision-makers' objectives. By incrementally querying preferences between pairs of elements, we iteratively refine the parametric uncertainty regions, leveraging the structural properties of matroids. Our method aims to achieve the exact optimum by reducing regret with a few elicitation rounds. Additionally, our approach avoids the computation of Minimax Regret and the use of Linear programming solvers at every iteration, unlike previous methods. Experimental results on four standard matroids demonstrate that our method reaches optimality more quickly and with fewer preference queries than existing techniques.

In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of linear Laplacian and simplified nonlinear terms, our method reduces the computational overhead typical of traditional Newton methods while handling the large, sparse matrices generated from discretized PDEs. We also provide a convergence analysis demonstrating local convergence to the exact solution under optimal choices for the regularization parameter, ensuring stability and efficiency in each iteration. Numerical experiments in two- and three-dimensional domains validate the proposed method's robustness and computational gains with tensor-product implementation. This approach offers a promising pathway for accelerating quasi-linear elliptic equation and system solvers, expanding the feasibility of complex simulations in physics, engineering, and other fields leveraging advanced hardware capabilities.

The partitioning of data for estimation and calibration critically impacts the performance of propensity score based estimators like inverse probability weighting (IPW) and double/debiased machine learning (DML) frameworks. We extend recent advances in calibration techniques for propensity score estimation, improving the robustness of propensity scores in challenging settings such as limited overlap, small sample sizes, or unbalanced data. Our contributions are twofold: First, we provide a theoretical analysis of the properties of calibrated estimators in the context of DML. To this end, we refine existing calibration frameworks for propensity score models, with a particular emphasis on the role of sample-splitting schemes in ensuring valid causal inference. Second, through extensive simulations, we show that calibration reduces variance of inverse-based propensity score estimators while also mitigating bias in IPW, even in small-sample regimes. Notably, calibration improves stability for flexible learners (e.g., gradient boosting) while preserving the doubly robust properties of DML. A key insight is that, even when methods perform well without calibration, incorporating a calibration step does not degrade performance, provided that an appropriate sample-splitting approach is chosen.

This paper attempts to jointly optimize the hybrid precoding (HP) and intelligent reflecting surfaces (IRS) beamforming matrices in a multi-IRS-aided mmWave communication network, utilizing the Alamouti scheme at the base station (BS). Considering the overall signal-to-noise ratio (SNR) as the objective function, the underlying problem is cast as an optimization problem, which is shown to be non-convex in general. To tackle the problem, noting that the unknown matrices contribute multiplicatively to the objective function, they are reformulated into two new matrices with rank constraints. Then, using the so-called inner approximation (IA) technique in conjunction with majorization-minimization (MM) approaches, these new matrices are solved iteratively. From one of these matrices, the IRS beamforming matrices can be effectively extracted. Meanwhile, HP precoding matrices can be solved separately through a new optimization problem aimed at minimizing the Euclidean distance between the fully digital (FD) precoder and HP analog/digital precoders. This is achieved through the use of a modified block coordinate descent (MBCD) algorithm. Simulation results demonstrate that the proposed algorithm outperforms various benchmark schemes in terms of achieving a higher achievable rate.

This paper investigates the asymptotic properties of least absolute deviation (LAD) regression for linear models with polynomial regressors, highlighting its robustness against heavy-tailed noise and outliers. Assuming independent and identically distributed (i.i.d.) errors, we establish the multiscale asymptotic normality of LAD estimators. A central result is the derivation of the asymptotic precision matrix, shown to be proportional to Hilbert matrices, with the proportionality coefficient depending on the asymptotic variance of the sample median of the noise distribution. We further explore the estimator's convergence properties, both in probability and almost surely, under varying model specifications. Through comprehensive simulations, we evaluate the speed of convergence of the LAD estimator and the empirical coverage probabilities of confidence intervals constructed under different scaling factors (T 1/2 and T $\alpha$ ). These experiments incorporate a range of noise distributions, including Laplace, Gaussian, and Cauchy, to demonstrate the estimator's robustness and efficiency. The findings underscore the versatility and practical relevance of LAD regression in handling non-standard data environments. By connecting the statistical properties of LAD estimators to classical mathematical structures, such as Hilbert matrices, this study offers both theoretical insights and practical tools for robust statistical modeling.

Communication compression is an essential strategy for alleviating communication overhead by reducing the volume of information exchanged between computing nodes in large-scale distributed stochastic optimization. Although numerous algorithms with convergence guarantees have been obtained, the optimal performance limit under communication compression remains unclear. In this paper, we investigate the performance limit of distributed stochastic optimization algorithms employing communication compression. We focus on two main types of compressors, unbiased and contractive, and address the best-possible convergence rates one can obtain with these compressors. We establish the lower bounds for the convergence rates of distributed stochastic optimization in six different settings, combining strongly-convex, generally-convex, or non-convex functions with unbiased or contractive compressor types. To bridge the gap between lower bounds and existing algorithms' rates, we propose NEOLITHIC, a nearly optimal algorithm with compression that achieves the established lower bounds up to logarithmic factors under mild conditions. Extensive experimental results support our theoretical findings. This work provides insights into the theoretical limitations of existing compressors and motivates further research into fundamentally new compressor properties.

In complex scenarios where typical pick-and-place techniques are insufficient, often non-prehensile manipulation can ensure that a robot is able to fulfill its task. However, non-prehensile manipulation is challenging due to its underactuated nature with hybrid-dynamics, where a robot needs to reason about an object's long-term behavior and contact-switching, while being robust to contact uncertainty. The presence of clutter in the workspace further complicates this task, introducing the need to include more advanced spatial analysis to avoid unwanted collisions. Building upon prior work on reinforcement learning with multimodal categorical exploration for planar pushing, we propose to incorporate location-based attention to enable robust manipulation in cluttered scenes. Unlike previous approaches addressing this obstacle avoiding pushing task, our framework requires no predefined global paths and considers the desired target orientation of the manipulated object. Experimental results in simulation as well as with a real KUKA iiwa robot arm demonstrate that our learned policy manipulates objects successfully while avoiding collisions through complex obstacle configurations, including dynamic obstacles, to reach the desired target pose.

This paper proposes an online inference method of the stochastic gradient descent (SGD) with a constant learning rate for quantile loss functions with theoretical guarantees. Since the quantile loss function is neither smooth nor strongly convex, we view such SGD iterates as an irreducible and positive recurrent Markov chain. By leveraging this interpretation, we show the existence of a unique asymptotic stationary distribution, regardless of the arbitrarily fixed initialization. To characterize the exact form of this limiting distribution, we derive bounds for its moment generating function and tail probabilities, controlling over the first and second moments of SGD iterates. By these techniques, we prove that the stationary distribution converges to a Gaussian distribution as the constant learning rate $\eta\rightarrow0$. Our findings provide the first central limit theorem (CLT)-type theoretical guarantees for the last iterate of constant learning-rate SGD in non-smooth and non-strongly convex settings. We further propose a recursive algorithm to construct confidence intervals of SGD iterates in an online manner. Numerical studies demonstrate strong finite-sample performance of our proposed quantile estimator and inference method. The theoretical tools in this study are of independent interest to investigate general transition kernels in Markov chains.

Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.