Related papers: Linear Bandit algorithms using the Bootstrap
This paper considers stochastic linear bandits with general nonlinear constraints. The objective is to maximize the expected cumulative reward over horizon $T$ subject to a set of constraints in each round $\tau\leq T$. We propose a…
Linear bandits have long been a central topic in online learning, with applications ranging from recommendation systems to adaptive clinical trials. Their general learnability has been established when the objective is to minimise the inner…
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,…
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…
We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context.…
We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the…
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…
We consider stochastic multi-armed bandit problems where the expected reward is a Lipschitz function of the arm, and where the set of arms is either discrete or continuous. For discrete Lipschitz bandits, we derive asymptotic problem…
Heavy-tailed bandits have been extensively studied since the seminal work of \citet{Bubeck2012BanditsWH}. In particular, heavy-tailed linear bandits, enabling efficient learning with both a large number of arms and heavy-tailed noises, have…
Cascading bandits is a natural and popular model that frames the task of learning to rank from Bernoulli click feedback in a bandit setting. For the case of unstructured rewards, we prove matching upper and lower bounds for the…
An agent in a nonstationary contextual bandit problem should balance between exploration and the exploitation of (periodic or structured) patterns present in its previous experiences. Handcrafting an appropriate historical context is an…
The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is…
This paper studies parametric bootstrap methods for network data, with the goal of quantifying the uncertainty of network statistics of interest. While existing network resampling methods primarily focus on count statistics under…
We study a stochastic convex bandit problem where the subgaussian noise parameter is assumed to decrease linearly as the learner selects actions closer and closer to the minimizer of the convex loss function. Accordingly, we propose a…
We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators…
In this paper, we investigate the stochastic contextual bandit with general function space and graph feedback. We propose an algorithm that addresses this problem by adapting to both the underlying graph structures and reward gaps. To the…
We consider the problem of adaptively placing sensors along an interval to detect stochastically-generated events. We present a new formulation of the problem as a continuum-armed bandit problem with feedback in the form of partial…
We consider a stochastic linear bandit problem in which the rewards are not only subject to random noise, but also adversarial attacks subject to a suitable budget $C$ (i.e., an upper bound on the sum of corruption magnitudes across the…
Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties…
In $\mathcal{X}$-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time…