Related papers: Sharp analysis of linear ensemble sampling

Restless bandit problems are instances of non-stationary multi-armed bandits. These problems have been studied well from the optimization perspective, where the goal is to efficiently find a near-optimal policy when system parameters are…

In a low-rank linear bandit problem, the reward of an action (represented by a matrix of size $d_1 \times d_2$) is the inner product between the action and an unknown low-rank matrix $\Theta^*$. We propose an algorithm based on a novel…

We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\top \theta$ where $\theta$ is sampled i.i.d. We show a regret upper bound of $\widetilde{O} (\sqrt{d T \log (K/\delta)…

Recent growing adoption of experimentation in practice has led to a surge of attention to multiarmed bandits as a technique to reduce the opportunity cost of online experiments. In this setting, a decision-maker sequentially chooses among a…

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,…

Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes…

Stochastic linear bandits are a natural and simple generalisation of finite-armed bandits with numerous practical applications. Current approaches focus on generalising existing techniques for finite-armed bandits, notably the optimism…

We prove that Thompson sampling exhibits $\tilde{O}(\sigma d \sqrt{T} + d r \sqrt{\mathrm{Tr}(\Sigma_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(\mu_0, \Sigma_0)$ prior distribution on the coefficients, where $d$…

We address online combinatorial optimization when the player has a prior over the adversary's sequence of losses. In this framework, Russo and Van Roy proposed an information-theoretic analysis of Thompson Sampling based on the information…

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…

We introduce the E$^4$ algorithm for the batched linear bandit problem, incorporating an Explore-Estimate-Eliminate-Exploit framework. With a proper choice of exploration rate, we prove E$^4$ achieves the finite-time minimax optimal regret…

We study stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for…

For the linear bandit problem, we extend the analysis of algorithm CombEXP from [R. Combes, M. S. Talebi Mazraeh Shahi, A. Proutiere, and M. Lelarge. Combinatorial bandits revisited. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and…

We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the…

Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $\Omega(n^{2/3})$ dimension-free minimax regret lower…

Bayesian bandit algorithms with approximate Bayesian inference have been widely used in real-world applications. Despite the superior practical performance, their theoretical justification is less investigated in the literature, especially…

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical…

We explore a stochastic contextual linear bandit problem where the agent observes a noisy, corrupted version of the true context through a noise channel with an unknown noise parameter. Our objective is to design an action policy that can…

This paper introduces and addresses a wide class of stochastic bandit problems where the function mapping the arm to the corresponding reward exhibits some known structural properties. Most existing structures (e.g. linear, Lipschitz,…

We study a noise model for linear stochastic bandits for which the subgaussian noise parameter vanishes linearly as we select actions on the unit sphere closer and closer to the unknown vector. We introduce an algorithm for this problem…