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The widespread adoption of distributed learning to train a global model from local data has been hindered by the challenge posed by stragglers. Recent attempts to mitigate this issue through gradient coding have proved difficult due to the large amounts of data redundancy, computational and communicational overhead it brings. Additionally, the complexity of encoding and decoding increases linearly with the number of local workers. In this paper, we present a lightweight coding method for the computing phase and a fair transmission protocol for the communication phase, to mitigate the straggler problem. A two-stage dynamic coding scheme is proposed for the computing phase, where partial gradients are computed by a portion of workers in the first stage and the remainder are decided based on their completion status in the first stage. To ensure fair communication, a perturbed Lyapunov function is designed to balance admission data fairness and maximize throughput. Extensive experimental results demonstrate the superiority of our proposed solution in terms of accuracy and resource utilization in the distributed learning system, even under practical network conditions and benchmark data.

In this paper, we propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection. The MRCT estimator employs a subset-based approach that prioritizes subsets exhibiting greater centrality based on the generalization of the Mahalanobis distance, resulting in a fast-MCD type algorithm. Notably, the MRCT estimator handles high-dimensional data sets without the need for preprocessing or dimension reduction techniques, due to the internal smoothening whose amount is determined by the regularization parameter $\alpha > 0$. The selection of the regularization parameter $\alpha$ is automated. The proposed method adapts seamlessly to sparsely observed data by working directly with the finite matrix of basis coefficients. An extensive simulation study demonstrates the efficacy of the MRCT estimator in terms of robust covariance estimation and automated outlier detection, emphasizing the balance between noise exclusion and signal preservation achieved through appropriate selection of $\alpha$. The method converges fast in practice and performs favorably when compared to other functional outlier detection methods.

Cardinality estimation methods based on probability distribution estimation have achieved high-precision estimation results compared to traditional methods. However, the most advanced methods suffer from high estimation costs due to the sampling method they use when dealing with range queries. Also, such a sampling method makes them difficult to differentiate, so the supervision signal from the query workload is difficult to train the model to improve the accuracy of cardinality estimation. In this paper, we propose a new hybrid and deterministic modeling approach (Duet) for the cardinality estimation problem which has better efficiency and scalability compared to previous approaches. Duet allows for direct cardinality estimation of range queries with significantly lower time and memory costs, as well as in a differentiable form. As the prediction process of this approach is differentiable, we can incorporate queries with larger model estimation errors into the training process to address the long-tail distribution problem of model estimation errors on high dimensional tables. We evaluate Duet on classical datasets and benchmarks, and the results prove the effectiveness of Duet.

Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR is critical but challenging. In this paper, we propose a new method called functional slicing-free inverse regression (FSFIR) to estimate the central subspace in FSDR. FSFIR is based on the martingale difference divergence operator, which is a novel metric introduced to characterize the conditional mean independence of a functional predictor on a multivariate response. We also provide a specific convergence rate for the FSFIR estimator. Compared with existing functional sliced inverse regression methods, FSFIR does not require the selection of a slice number. Simulations demonstrate the efficiency and convenience of FSFIR.

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of solutions across neighboring subdomains, we adopt a generalized Robin-type interface condition, assigning unique Robin parameters to each subdomain. These subdomain-specific Robin parameters are learned to minimize the mismatch on the Robin interface condition, facilitating efficient information exchange during training. Our method is applicable to both the Laplace's and Helmholtz equations. It represents local solutions by an independent neural network model which is trained to minimize the loss on the governing PDE while strictly enforcing boundary and interface conditions through an augmented Lagrangian formalism. A key strength of our method lies in its ability to learn a Robin parameter for each subdomain, thereby enhancing information exchange with its neighboring subdomains. We observe that the learned Robin parameters adapt to the local behavior of the solution, domain partitioning and subdomain location relative to the overall domain. Extensive experiments on forward and inverse problems, including one-way and two-way decompositions with crosspoints, demonstrate the versatility and performance of our proposed approach.

This paper is concerned with the issue of improving video subscribers' quality of experience (QoE) by deploying a multi-unmanned aerial vehicle (UAV) network. Different from existing works, we characterize subscribers' QoE by video bitrates, latency, and frame freezing and propose to improve their QoE by energy-efficiently and dynamically optimizing the multi-UAV network in terms of serving UAV selection, UAV trajectory, and UAV transmit power. The dynamic multi-UAV network optimization problem is formulated as a challenging sequential-decision problem with the goal of maximizing subscribers' QoE while minimizing the total network power consumption, subject to some physical resource constraints. We propose a novel network optimization algorithm to solve this challenging problem, in which a Lyapunov technique is first explored to decompose the sequential-decision problem into several repeatedly optimized sub-problems to avoid the curse of dimensionality. To solve the sub-problems, iterative and approximate optimization mechanisms with provable performance guarantees are then developed. Finally, we design extensive simulations to verify the effectiveness of the proposed algorithm. Simulation results show that the proposed algorithm can effectively improve the QoE of subscribers and is 66.75\% more energy-efficient than benchmarks.

In this work, we give a statistical characterization of the $\gamma$-regret for arbitrary structured bandit problems, the regret which arises when comparing against a benchmark that is $\gamma$ times the optimal solution. The $\gamma$-regret emerges in structured bandit problems over a function class $\mathcal{F}$ where finding an exact optimum of $f \in \mathcal{F}$ is intractable. Our characterization is given in terms of the $\gamma$-DEC, a statistical complexity parameter for the class $\mathcal{F}$, which is a modification of the constrained Decision-Estimation Coefficient (DEC) of Foster et al., 2023 (and closely related to the original offset DEC of Foster et al., 2021). Our lower bound shows that the $\gamma$-DEC is a fundamental limit for any model class $\mathcal{F}$: for any algorithm, there exists some $f \in \mathcal{F}$ for which the $\gamma$-regret of that algorithm scales (nearly) with the $\gamma$-DEC of $\mathcal{F}$. We provide an upper bound showing that there exists an algorithm attaining a nearly matching $\gamma$-regret. Due to significant challenges in applying the prior results on the DEC to the $\gamma$-regret case, both our lower and upper bounds require novel techniques and a new algorithm.

In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation. We focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative $\ell_1$ penalty model for the considered problem, which penalizes the one-bit constraint into the objective by a negative $\ell_1$-norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating proximal/projection gradient descent ascent (APGDA) algorithm for solving it, which performs a proximal gradient decent over one block of variables and a projection gradient ascent over the other block of variables alternately. The APGDA algorithm enjoys a low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the APGDA algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared to the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost.

Parameter Efficient Tuning (PET) has gained attention for reducing the number of parameters while maintaining performance and providing better hardware resource savings, but few studies investigate dense prediction tasks and interaction between modalities. In this paper, we do an investigation of efficient tuning problems on referring image segmentation. We propose a novel adapter called Bridger to facilitate cross-modal information exchange and inject task-specific information into the pre-trained model. We also design a lightweight decoder for image segmentation. Our approach achieves comparable or superior performance with only 1.61\% to 3.38\% backbone parameter updates, evaluated on challenging benchmarks. The code is available at \url{//github.com/kkakkkka/ETRIS}.

A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the problem and by applying the finite element method. To obtain the lower bounds we formulate the dual variational problem and introduce appropriate approximation spaces employing the finite element method as well. We deal with the 3D setting, which has been rarely considered in the literature so far. The theoretical justification of the procedure is presented and supported with illustrative examples.