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Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…
Contextual linear dueling bandits have recently garnered significant attention due to their widespread applications in important domains such as recommender systems and large language models. Classical dueling bandit algorithms are…
We study distributed adversarial bandits, where $N$ agents cooperate to minimize the global average loss while observing only their own local losses. We show that the minimax regret for this problem is…
Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…
In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds. In this paper we further our understanding of these concepts in the…
In this paper, we introduce a distributed version of the classical stochastic Multi-Arm Bandit (MAB) problem. Our setting consists of a large number of agents $n$ that collaboratively and simultaneously solve the same instance of $K$ armed…
We consider the problem where M agents collaboratively interact with an instance of a stochastic K-armed contextual bandit, where K>>M. The goal of the agents is to simultaneously minimize the cumulative regret over all the agents over a…
This paper introduces a federated learning framework tailored for online combinatorial optimization with bandit feedback. In this setting, agents select subsets of arms, observe noisy rewards for these subsets without accessing individual…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal non-private…
We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number…
Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance…
Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in…
Decision-makers often simultaneously face many related but heterogeneous learning problems. For instance, a large retailer may wish to learn product demand at different stores to solve pricing or inventory problems, making it desirable to…
It is well-known that for sparse linear bandits, when ignoring the dependency on sparsity which is much smaller than the ambient dimension, the worst-case minimax regret is $\widetilde{\Theta}\left(\sqrt{dT}\right)$ where $d$ is the ambient…
Stochastic sparse linear bandits offer a practical model for high-dimensional online decision-making problems and have a rich information-regret structure. In this work we explore the use of information-directed sampling (IDS), which…
We study collaborative learning in multi-agent Bayesian bandit problems, where strategic agents collectively solve the same bandit instance. While multiple agents can accelerate learning by sharing information, strategic agents might prefer…
Generalized linear bandits have been extensively studied due to their broad applicability in real-world online decision-making problems. However, these methods typically assume that the expected reward function is known to the users, an…
Contextual bandit with linear reward functions is among one of the most extensively studied models in bandit and online learning research. Recently, there has been increasing interest in designing \emph{locally private} linear contextual…