Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

Recall thatx = argmina Ax>θ so x can be viewed as a deterministic functionθ . " log p(zn|θ) (1/|Nε|) P Since Rmax is the upper bound of maximum expected reward, the second term can be bounded 2Rmaxγ. We letΦ R|A| d as the feature matrix where each row ofΦrepresent each action inA. We summarize the procedure of estimating t,It inAlgorithm3. LetX denote the feasible set.

Modern deep neural networks exhibit strong generalization even in highly overparameterized regimes. Significant progress has been made to understand this phenomenon in the context of supervised learning, but for unsupervised tasks such as denoising, several open questions remain. While some recent works have successfully characterized the test error of the linear denoising problem, they are limited to linear models (one-layer network). In this work, we focus on two-layer linear denoising autoencoders trained under gradient flow, incorporating two key ingredients of modern deep learning architectures: A low-dimensional bottleneck layer that effectively enforces a rank constraint on the learned solution, as well as the possibility of a skip connection that bypasses the bottleneck. We derive closed-form expressions for all critical points of this model under product regularization, and in particular describe its global minimizer under the minimum-norm principle. From there, we derive the test risk formula in the overparameterized regime, both for models with and without skip connections. Our analysis reveals two interesting phenomena: Firstly, the bottleneck layer introduces an additional complexity measure akin to the classical bias-variance trade-off -- increasing the bottleneck width reduces bias but introduces variance, and vice versa. Secondly, skip connection can mitigate the variance in denoising autoencoders -- especially when the model is mildly overparameterized. We further analyze the impact of skip connections in denoising autoencoder using random matrix theory and support our claims with numerical evidence.

The paper develops a connection between traditional perceptron algorithms and recently introduced herding algorithms. It is shown that both algorithms can be viewed as an application of the perceptron cycling theorem. This connection strengthens some herding results and suggests new (supervised) herding algorithms that, like CRFs or discriminative RBMs, make predictions by conditioning on the input attributes. We develop and investigate variants of conditional herding, and show that conditional herding leads to practical algorithms that perform better than or on par with related classifiers such as the voted perceptron and the discriminative RBM.

We introduce OmniRL, a highly generalizable in-context reinforcement learning (ICRL) model that is meta-trained on hundreds of thousands of diverse tasks. These tasks are procedurally generated by randomizing state transitions and rewards within Markov Decision Processes. To facilitate this extensive meta-training, we propose two key innovations: 1. An efficient data synthesis pipeline for ICRL, which leverages the interaction histories of diverse behavior policies; and 2. A novel modeling framework that integrates both imitation learning and reinforcement learning (RL) within the context, by incorporating prior knowledge. For the first time, we demonstrate that in-context learning (ICL) alone, without any gradient-based fine-tuning, can successfully tackle unseen Gymnasium tasks through imitation learning, online RL, or offline RL. Additionally, we show that achieving generalized ICRL capabilities-unlike task identification-oriented few-shot learning-critically depends on long trajectories generated by variant tasks and diverse behavior policies. By emphasizing the potential of ICL and departing from pre-training focused on acquiring specific skills, we further underscore the significance of meta-training aimed at cultivating the ability of ICL itself.

Random matrix theory has proven to be a valuable tool in analyzing the generalization of linear models. However, the generalization properties of even two-layer neural networks trained by gradient descent remain poorly understood. To understand the generalization performance of such networks, it is crucial to characterize the spectrum of the feature matrix at the hidden layer. Recent work has made progress in this direction by describing the spectrum after a single gradient step, revealing a spiked covariance structure. Y et, the generalization error for linear models with spiked covariances has not been previously determined. We derive their generalization error in the asymptotic proportional regime. Our analysis demonstrates that the eigenvector and eigenvalue corresponding to the spike significantly influence the generalization error. Significant theoretical work has been dedicated to understanding generalization in linear regression models (Dobriban & Wager, 2018; Advani et al., 2020; Mel & Ganguli, 2021; Derezinski et al., 2020; Hastie et al., 2022; Kausik et al., 2024; Wang et al., 2024a). For the random features approximation, the first layer of the neural network is considered fixed, and only the outer layer is trained. It has been shown that to understand the generalization, we need to analyze the distribution of singular values of F . Works such as Pennington & Worah (2017); Adlam et al. (2019); Benigni & Péché (2021); Fan & Wang (2020); Wang & Zhu (2024); Péché (2019); Piccolo & Schröder (2021) have studied the spectrum of F in the asymptotic limit, enabling us to understand the generalization. However, random feature models do not leverage the feature learning capabilities of neural networks. To gain further insights into the performance of two-layer neural networks and their feature learning capabilities, we need to train the inner layer. Recent studies such as Ba et al. (2022); Moniri et al. (2023) have examined the effects on F of taking one gradient step for the inner layer. Specifically, Ba et al. (2022) showed that with a sufficiently large step size η, two-layer models can already outperform random feature models after just one step. Moniri et al. (2023) extended this work to study many different scales for the step size. The bulk corresponds to F 0, while the spikes represent the effect of P .

Text style transfer (TST) is an important task in controllable text generation, which aims to control selected attributes of language use, such as politeness, formality, or sentiment, without altering the style-independent content of the text. The field has received considerable research attention in recent years and has already been covered in several reviews, but the focus has mostly been on the development of new algorithms and learning from different types of data (supervised, unsupervised, out-of-domain, etc.) and not so much on the application side. However, TST-related technologies are gradually reaching a production- and deployment-ready level, and therefore, the inclusion of the application perspective in TST research becomes crucial. Similarly, the often overlooked ethical considerations of TST technology have become a pressing issue. This paper presents a comprehensive review of TST applications that have been researched over the years, using both traditional linguistic approaches and more recent deep learning methods. We discuss current challenges, future research directions, and ethical implications of TST applications in text generation. By providing a holistic overview of the landscape of TST applications, we hope to stimulate further research and contribute to a better understanding of the potential as well as ethical considerations associated with TST.