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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…
Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online…
We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
We study the recovering bandits problem, a variant of the stochastic multi-armed bandit problem where the expected reward of each arm varies according to some unknown function of the time since the arm was last played. While being a natural…
Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under…
In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting…
We consider a multi-armed bandit problem where payoffs are a linear function of an observed stochastic contextual variable. In the scenario where there exists a gap between optimal and suboptimal rewards, several algorithms have been…
We consider distributed linear bandits where $M$ agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink…
Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…
The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…
Decision-making under uncertainty is a fundamental problem encountered frequently and can be formulated as a stochastic multi-armed bandit problem. In the problem, the learner interacts with an environment by choosing an action at each…
High-dimensional linear bandits with low-dimensional structure have received considerable attention in recent studies due to their practical significance. The most common structure in the literature is sparsity. However, it may not be…
Causal knowledge about the relationships among decision variables and a reward variable in a bandit setting can accelerate the learning of an optimal decision. Current works often assume the causal graph is known, which may not always be…
In this paper, we study sequential decision-making for maximizing the Sharpe ratio (SR) in a stochastic multi-armed bandit (MAB) setting. Unlike standard bandit formulations that maximize cumulative reward, SR optimization requires…
Most bandit policies are designed to either minimize regret in any problem instance, making very few assumptions about the underlying environment, or in a Bayesian sense, assuming a prior distribution over environment parameters. The former…
Many works have developed no-regret algorithms for contextual bandits with function approximation, where the mean reward function over context-action pairs belongs to a function class. Although there are many approaches to this problem, one…
We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by…
Online decision-making can be formulated as the popular stochastic multi-armed bandit problem where a learner makes decisions (or takes actions) to maximize cumulative rewards collected from an unknown environment. This paper proposes to…