February 2026

arXiv:2510.24710v3 Announce Type: replace-cross Abstract: We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with the Hessian matrix, we utilize penalty and augmented Lagrangian methods to reformulate the original problem as a single-level one. Especially, we establish a strong theoretical connection between the reformulated function and the original hyper-objective by characterizing the closeness of their values and […]

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arXiv:2510.22031v2 Announce Type: replace-cross Abstract: Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable $d$-separation scores, obtained through […]

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arXiv:2510.18713v3 Announce Type: replace-cross Abstract: We study online preference-based reinforcement learning (PbRL) with the goal of improving sample efficiency. While a growing body of theoretical work has emerged-motivated by PbRL’s recent empirical success, particularly in aligning large language models (LLMs)-most existing studies focus only on pairwise comparisons. A few recent works (Zhu et al., 2023, Mukherjee et al., 2024, Thekumparampil et al., 2024) have explored using multiple comparisons and ranking feedback, but their performance guarantees fail to improve-and […]

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arXiv:2509.26000v2 Announce Type: replace-cross Abstract: Asymmetric actor-critic methods are widely used in partially observable reinforcement learning, but typically assume full state observability to condition the critic during training, which is often unrealistic in practice. We introduce the informed asymmetric actor-critic framework, allowing the critic to be conditioned on arbitrary state-dependent privileged signals without requiring access to the full state. We show that any such privileged signal yields unbiased policy gradient estimates, substantially expanding the set of admissible privileged […]

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arXiv:2509.06505v2 Announce Type: replace-cross Abstract: The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision tasks, selecting their parameters often needs an exhaustive search, and only a few selection methods have been proven to be theoretically optimal. One of the most promising GAN variants is the Wasserstein GAN (WGAN). Prior work on optimal parameters for […]

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arXiv:2508.21022v2 Announce Type: replace-cross Abstract: Subsampled natural gradient descent (SNG) has been used to enable high-precision scientific machine learning, but standard analyses based on stochastic preconditioning fail to provide insight into realistic small-sample settings. We overcome this limitation by instead analyzing SNG as a sketch-and-project method. Motivated by this lens, we discard the usual theoretical proxy which decouples gradients and preconditioners using two independent mini-batches, and we replace it with a new proxy based on squared volume sampling. […]

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arXiv:2508.06483v2 Announce Type: replace-cross Abstract: We study the self-normalized concentration of vector-valued stochastic processes. We focus on bounds for “sub-$psi$” processes, a well-known and quite general class of process that encompasses a wide variety of well-known tail conditions (including sub-exponential, sub-Gaussian, sub-gamma, sub-Poisson, and several heavy-tailed settings without a moment generating function such as symmetric or bounded 2nd or 3rd moments). Our results recover and generalize the influential bound of de la Pe~na et al. [20] (proved again […]

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arXiv:2508.00120v2 Announce Type: replace-cross Abstract: Multimodal high-dimensional data are increasingly prevalent in biomedical research, yet they are often compromised by block-wise missingness and measurement errors, posing significant challenges for statistical inference and prediction. We propose AdapDISCOM, a novel adaptive direct sparse regression method that simultaneously addresses these two pervasive issues. Building on the DISCOM framework, AdapDISCOM introduces modality-specific weighting schemes to account for heterogeneity in data structures and error magnitudes across modalities. We establish the theoretical properties of […]

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arXiv:2506.12176v4 Announce Type: replace-cross Abstract: In explainable AI, surrogate models are commonly evaluated by their fidelity to a neural network’s predictions. Fidelity, however, measures alignment to a learned model rather than alignment to the data-generating signal underlying the task. This work introduces the linearity score $lambda(f)$, a diagnostic that quantifies the extent to which a regression network’s input–output behavior is linearly decodable. $lambda(f)$ is defined as an $R^2$ measure of surrogate fit to the network. Across synthetic and […]

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arXiv:2505.21799v4 Announce Type: replace-cross Abstract: The ever-growing scale of deep learning models and training data underscores the critical importance of efficient optimization methods. While preconditioned gradient methods such as Adam and AdamW are the de facto optimizers for training neural networks and large language models, structure-aware preconditioned optimizers like Shampoo and Muon, which utilize the matrix structure of gradients, have demonstrated promising evidence of faster convergence. In this paper, we introduce a unifying framework for analyzing “matrix-aware” preconditioned […]

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