Related papers: When can the two-armed bandit algorithm be trusted…
We consider minimisation of dynamic regret in non-stationary bandits with a slowly varying property. Namely, we assume that arms' rewards are stochastic and independent over time, but that the absolute difference between the expected…
We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model.…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result,…
We consider the two-armed bandit problem as applied to data processing if there are two alternative processing methods available with different a priori unknown efficiencies. One should determine the most effective method and provide its…
We propose a new strategy for best-arm identification with fixed confidence of Gaussian variables with bounded means and unit variance. This strategy, called Exploration-Biased Sampling, is not only asymptotically optimal: it is to the best…
Bandit algorithms are widely used in sequential decision problems to maximize the cumulative reward. One potential application is mobile health, where the goal is to promote the user's health through personalized interventions based on user…
We study pure exploration with infinitely many bandit arms generated i.i.d. from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$…
In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…
We study the problem of pure exploration in matching markets under uncertain preferences, where the goal is to identify a stable matching with confidence parameter $\delta$ and minimal sample complexity. Agents learn preferences via…
Contextual multi-armed bandit algorithms are widely used in sequential decision tasks such as news article recommendation systems, web page ad placement algorithms, and mobile health. Most of the existing algorithms have regret proportional…
The least-squares estimator has achieved considerable success in learning linear dynamical systems from a single trajectory of length $T$. While it attains an optimal error of $\mathcal{O}(1/\sqrt{T})$ under independent zero-mean noise, it…
We study the $K$-armed dueling bandit problem, a variation of the traditional multi-armed bandit problem in which feedback is obtained in the form of pairwise comparisons. Previous learning algorithms have focused on the $\textit{fully…
We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new {\em Regularized…
We consider the closely related problems of bandit convex optimization with two-point feedback, and zero-order stochastic convex optimization with two function evaluations per round. We provide a simple algorithm and analysis which is…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
Stochastic linear contextual bandit algorithms have substantial applications in practice, such as recommender systems, online advertising, clinical trials, etc. Recent works show that optimal bandit algorithms are vulnerable to adversarial…
Statistical inference from data generated by multi-armed bandit (MAB) algorithms is challenging due to their adaptive, non-i.i.d. nature. A classical manifestation is that sample averages of arm rewards under bandit sampling may fail to…
We study the problem of characterizing optimal learning algorithms for playing repeated games against an adversary with unknown payoffs. In this problem, the first player (called the learner) commits to a learning algorithm against a second…
This study presents two new algorithms for solving linear stochastic bandit problems. The proposed methods use an approach from non-parametric statistics called bootstrapping to create confidence bounds. This is achieved without making any…