Instrumental variables (IV) estimation, also known as IV regression, is a fundamental method in econometrics and statistics to infer causal relationships in observational data with unobserved confounding. It leverages access to additional variables (instruments) that affect the outcome exogenously and exclusively through the endogenous regressor to yield consistent causal estimates, even when the standard ordinary least squares (OLS) estimator is biased by unobserved confounding (Imbens and Angrist, 1994; Angrist et al., 1996; Imbens and Rubin, 2015). Over the years, IV estimation has become an indispensable tool for causal inference in empirical works in economics (Card and Krueger, 1994), as well as in the study of genetic and epidemiological data (Davey Smith and Ebrahim, 2003). Despite the widespread use of IV in empirical and applied works, it has important limitations and challenges, such as invalid instruments (Sargan, 1958; Murray, 2006), weak instruments (Staiger and Stock, 1997), non-compliance (Imbens and Angrist, 1994), and heteroskedasticity, especially in settings with weak instruments or highly leveraged datasets (Andrews et al., 2019; Young, 2022). These issues could significantly impact the validity and quality of estimation and inference using instrumental variables (Jiang, 2017). Many works have since been devoted to assessing and addressing these issues, such as statistical tests (Hansen, 1982; Stock and Yogo, 2002), sensitivity analysis (Rosenbaum and Rubin, 1983; Bonhomme and Weidner, 2022), and additional assumptions or structures on the data generating process (Kolesár et al., 2015; Kang et al., 2016; Guo et al., 2018b). Recently, an emerging line of works have highlighted interesting connections between causality and the concepts of invariance and robustness (Peters et al., 2016; Meinshausen, 2018; Rothenhäusler et al., 2021; Bühlmann, 2020; Jakobsen and Peters, 2022; Fan et al., 2024). Their guiding philosophy is that causal properties can be viewed as robustness against changes across heterogeneous environments, represented by a set P of data distributions.

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times.

Non-smooth communication-efficient federated optimization is crucial for many machine learning applications, yet remains largely unexplored theoretically. Recent advancements have primarily focused on smooth convex and non-convex regimes, leaving a significant gap in understanding the non-smooth convex setting. Additionally, existing literature often overlooks efficient server-to-worker communication (downlink), focusing primarily on worker-to-server communication (uplink). We consider a setup where uplink costs are negligible and focus on optimizing downlink communication by improving state-of-the-art schemes like EF21-P (arXiv:2209.15218) and MARINA-P (arXiv:2402.06412) in the non-smooth convex setting. We extend the non-smooth convex theory of EF21-P [Anonymous, 2024], originally developed for single-node scenarios, to the distributed setting, and extend MARINA-P to the non-smooth convex setting. For both algorithms, we prove an optimal $O(1/\sqrt{T})$ convergence rate and establish communication complexity bounds matching classical subgradient methods. We provide theoretical guarantees under constant, decreasing, and adaptive (Polyak-type) stepsizes. Our experiments demonstrate that MARINA-P with correlated compressors outperforms other methods in both smooth non-convex and non-smooth convex settings. This work presents the first theoretical results for distributed non-smooth optimization with server-to-worker compression, along with comprehensive analysis for various stepsize schemes.

We introduce a multi-modal autonomous delivery optimization framework as a coalition game for a fleet of UAVs and ADRs operating in two overlaying networks to address last-mile delivery in urban environments, including high-density areas, road-based routing, and real-world operational challenges. The problem is defined as multiple depot pickup and delivery with time windows constrained over operational restrictions, such as vehicle battery limitation, precedence time window, and building obstruction. Subsequently, the coalition game theory is applied to investigate cooperation structures among the modes to capture how strategic collaboration among vehicles can improve overall routing efficiency. To do so, a generalized reinforcement learning model is designed to evaluate the cost-sharing and allocation to different coalitions for which sub-additive property and non-empty core exist. Our methodology leverages an end-to-end deep multi-agent policy gradient method augmented by a novel spatio-temporal adjacency neighbourhood graph attention network and transformer architecture using a heterogeneous edge-enhanced attention model. Conducting several numerical experiments on last-mile delivery applications, the result from the case study in the city of Mississauga shows that despite the incorporation of an extensive network in the graph for two modes and a complex training structure, the model addresses realistic operational constraints and achieves high-quality solutions compared with the existing transformer-based and heuristics methods and can perform well on non-homogeneous data distribution, generalizes well on the different scale and configuration, and demonstrate a robust performance under stochastic scenarios subject to wind speed and direction.

To bridge the digital divide, the space-ground integrated networks (SGINs), which will be a key component of the six-generation (6G) mobile networks, are expected to deliver artificial intelligence (AI) services to every corner of the world. One mission of SGINs is to support federated learning (FL) at a global scale. However, existing space-ground integrated FL frameworks involve ground stations or costly inter-satellite links, entailing excessive training latency and communication costs. To overcome these limitations, we propose an infrastructure-free federated learning framework based on a model dispersal (FedMeld) strategy, which exploits periodic movement patterns and store-carry-forward capabilities of satellites to enable parameter mixing across large-scale geographical regions. We theoretically show that FedMeld leads to global model convergence and quantify the effects of round interval and mixing ratio between adjacent areas on its learning performance. Based on the theoretical results, we formulate a joint optimization problem to design the staleness control and mixing ratio (SC-MR) for minimizing the training loss. By decomposing the problem into sequential SC and MR subproblems without compromising the optimality, we derive the round interval solution in a closed form and the mixing ratio in a semi-closed form to achieve the \textit{optimal} latency-accuracy tradeoff. Experiments using various datasets demonstrate that FedMeld achieves superior model accuracy while significantly reducing communication costs as compared with traditional FL schemes for SGINs.

Index tracking is a popular passive investment strategy aimed at optimizing portfolios, but fully replicating an index can lead to high transaction costs. To address this, partial replication have been proposed. However, the cardinality constraint renders the problem non-convex, non-differentiable, and often NP-hard, leading to the use of heuristic or neural network-based methods, which can be non-interpretable or have NP-hard complexity. To overcome these limitations, we propose a Differentiable Cardinality Constraint ($\textbf{DCC}$) for index tracking and introduce a floating-point precision-aware method ($\textbf{DCC}_{fpp}$) to address implementation issues. We theoretically prove our methods calculate cardinality accurately and enforce actual cardinality with polynomial time complexity. We propose the range of the hyperparameter $a$ ensures that $\textbf{DCC}_{fpp}$ has no error in real implementations, based on theoretical proof and experiment. Our method applied to mathematical method outperforms baseline methods across various datasets, demonstrating the effectiveness of the identified hyperparameter $a$.

We introduce \textbf{Gr}adient Descent with \textbf{A}daptive \textbf{M}omentum \textbf{S}caling (\textbf{Grams}), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

Imperceptible adversarial attacks have recently attracted increasing research interests. Existing methods typically incorporate external modules or loss terms other than a simple $l_p$-norm into the attack process to achieve imperceptibility, while we argue that such additional designs may not be necessary. In this paper, we rethink the essence of imperceptible attacks and propose two simple yet effective strategies to unleash the potential of PGD, the common and classical attack, for imperceptibility from an optimization perspective. Specifically, the Dynamic Step Size is introduced to find the optimal solution with minimal attack cost towards the decision boundary of the attacked model, and the Adaptive Early Stop strategy is adopted to reduce the redundant strength of adversarial perturbations to the minimum level. The proposed PGD-Imperceptible (PGD-Imp) attack achieves state-of-the-art results in imperceptible adversarial attacks for both untargeted and targeted scenarios. When performing untargeted attacks against ResNet-50, PGD-Imp attains 100$\%$ (+0.3$\%$) ASR, 0.89 (-1.76) $l_2$ distance, and 52.93 (+9.2) PSNR with 57s (-371s) running time, significantly outperforming existing methods.

Bayesian Optimization (BO) is a popular approach to optimizing expensive-to-evaluate black-box functions. Despite the success of BO, its performance may decrease exponentially as the dimensionality increases. A common framework to tackle this problem is to assume that the objective function depends on a limited set of features that lie on a low-dimensional manifold embedded in the high-dimensional ambient space. The latent space can be linear or more generally nonlinear. To learn feature mapping, existing works usually use an encode-decoder framework which is either computationally expensive or susceptible to overfittting when the labeled data is limited. This paper proposes a new approach for BO in high dimensions by exploiting a new representation of the objective function. Our approach combines a random linear projection to reduce the dimensionality, with a representation learning of the nonlinear manifold. When the geometry of the latent manifold is available, a solution to exploit this geometry is proposed for representation learning. In contrast, we use a neural network. To mitigate overfitting by using the neural network, we train the feature mapping in a geometry-aware semi-supervised manner. Our approach enables efficient optimizing of BO's acquisition function in the low-dimensional space, with the advantage of projecting back to the original high-dimensional space compared to existing works in the same setting. Finally, we show empirically that our algorithm outperforms other high-dimensional BO baselines in various synthetic functions and real applications.

Robotic dexterous grasping is a key step toward human-like manipulation. To fully unleash the potential of data-driven models for dexterous grasping, a large-scale, high-quality dataset is essential. While gradient-based optimization offers a promising way for constructing such datasets, existing works suffer from limitations, such as restrictive assumptions in energy design or limited experiments on small object sets. Moreover, the lack of a standard benchmark for comparing synthesis methods and datasets hinders progress in this field. To address these challenges, we develop a highly efficient synthesis system and a comprehensive benchmark with MuJoCo for dexterous grasping. Our system formulates grasp synthesis as a bilevel optimization problem, combining a novel lower-level quadratic programming (QP) with an upper-level gradient descent process. By leveraging recent advances in CUDA-accelerated robotic libraries and GPU-based QP solvers, our system can parallelize thousands of grasps and synthesize over 49 grasps per second on a single NVIDIA 3090 GPU. Our synthesized grasps for Shadow Hand and Allegro Hand achieve a success rate above 75% in MuJoCo, with a penetration depth and contact distance of under 1 mm, outperforming existing baselines on nearly all metrics. Compared to the previous large-scale dataset, DexGraspNet, our dataset significantly improves the performance of learning models, with a simulation success rate from around 40% to 80%. Real-world testing of the trained model on the Shadow Hand achieves an 81% success rate across 20 diverse objects.