Related papers: On High-dimensional and Low-rank Tensor Bandits

This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. We integrate the $\varepsilon$-greedy bandit algorithm for…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm,…

An individual's decisions are often guided by those of his or her peers, i.e., neighbors in a social network. Presumably, being privy to the experiences of others aids in learning and decision making, but how much advantage does an…

This work tackles the complexities of multi-player scenarios in \emph{unknown games}, where the primary challenge lies in navigating the uncertainty of the environment through bandit feedback alongside strategic decision-making. We…

The literature on bandit learning and regret analysis has focused on contexts where the goal is to converge on an optimal action in a manner that limits exploration costs. One shortcoming imposed by this orientation is that it does not…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Thompson Sampling, one of the oldest heuristics for solving multi-armed bandits, has recently been shown to demonstrate state-of-the-art performance. The empirical success has led to great interests in theoretical understanding of this…

Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…

In this research, we investigate the high-dimensional linear contextual bandit problem where the number of features $p$ is greater than the budget $T$, or it may even be infinite. Differing from the majority of previous works in this field,…

Contextual dueling bandits form a cornerstone of preference-based decision-making, with critical applications in recommender systems and large language model alignment. However, standard algorithms rely on the idealized assumption of…

Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are $L$ observed contexts and $K$ arms of the bandit. The…

The multi-armed bandits' framework is the most common platform to study strategies for sequential decision-making problems. Recently, the notion of fairness has attracted a lot of attention in the machine learning community. One can impose…

Random embedding has been applied with empirical success to large-scale black-box optimization problems with low effective dimensions. This paper proposes the EmbeddedHunter algorithm, which incorporates the technique in a hierarchical…

A challenging aspect of the bandit problem is that a stochastic reward is observed only for the chosen arm and the rewards of other arms remain missing. The dependence of the arm choice on the past context and reward pairs compounds the…

We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with…