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

In sparse linear bandits, a learning agent sequentially selects an action and receive reward feedback, and the reward function depends linearly on a few coordinates of the covariates of the actions. This has applications in many real-world…

We study model selection in linear bandits, where the learner must adapt to the dimension (denoted by $d_\star$) of the smallest hypothesis class containing the true linear model while balancing exploration and exploitation. Previous papers…

Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward…

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Tree-form sequential decision making (TFSDM) extends classical one-shot decision making by modeling tree-form interactions between an agent and a potentially adversarial environment. It captures the online decision-making problems that each…

We consider the stochastic contextual bandit problem under the high dimensional linear model. We focus on the case where the action space is finite and random, with each action associated with a randomly generated contextual covariate. This…

Bandit algorithms have various application in safety-critical systems, where it is important to respect the system constraints that rely on the bandit's unknown parameters at every round. In this paper, we formulate a linear stochastic…

We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension:…

We consider a stochastic linear bandit model in which the available actions correspond to arbitrary context vectors whose associated rewards follow a non-stationary linear regression model. In this setting, the unknown regression parameter…

In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…

We study the stochastic contextual bandit problem, where the reward is generated from an unknown function with additive noise. No assumption is made about the reward function other than boundedness. We propose a new algorithm, NeuralUCB,…

We study a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the reward generating function is unknown. We propose a novel learning algorithm that transforms the raw feature…

We study high-dimensional multi-armed contextual bandits with batched feedback where the $T$ steps of online interactions are divided into $L$ batches. In specific, each batch collects data according to a policy that depends on previous…

Policy regret is a well established notion of measuring the performance of an online learning algorithm against an adaptive adversary. We study restrictions on the adversary that enable efficient minimization of the \emph{complete policy…

We study a stochastic bandit problem with a general unknown reward function and a general unknown constraint function. Both functions can be non-linear (even non-convex) and are assumed to lie in a reproducing kernel Hilbert space (RKHS)…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We study a collaborative multi-agent stochastic linear bandit setting, where $N$ agents that form a network communicate locally to minimize their overall regret. In this setting, each agent has its own linear bandit problem (its own reward…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

In this work we revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits, from the perspective of adversarial robustness. Existing works in algorithmic robust statistics make strong…