Related papers: Sequential estimation of quantiles with applicatio…

We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial…

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…

We consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148-177], based on…

We lay the foundations of a non-parametric theory of best-arm identification in multi-armed bandits with a fixed budget T. We consider general, possibly non-parametric, models D for distributions over the arms; an overarching example is the…

In fixed budget bandit identification, an algorithm sequentially observes samples from several distributions up to a given final time. It then answers a query about the set of distributions. A good algorithm will have a small probability of…

The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be…

We consider the problem of finding, through adaptive sampling, which of $n$ options (arms) has the largest mean. Our objective is to determine a rule which identifies the best arm with a fixed minimum confidence using as few observations as…

Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential…

We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be…

In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are…

Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as…

We focus on the problem of best-arm identification in a stochastic multi-arm bandit with temporally decreasing variances for the arms' rewards. We model arm rewards as Gaussian random variables with fixed means and variances that decrease…

Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…

We study best arm identification in a restless multi-armed bandit setting with finitely many arms. The discrete-time data generated by each arm forms a homogeneous Markov chain taking values in a common, finite state space. The state…

In this paper we consider the problem of estimating quantiles when data are received sequentially (data stream). For real life data streams, the distribution of the data typically varies with time making estimation of quantiles challenging.…

We consider the best-arm identification problem in multi-armed bandits, which focuses purely on exploration. A player is given a fixed budget to explore a finite set of arms, and the rewards of each arm are drawn independently from a fixed,…

Adaptive experiments are used extensively in online platforms, healthcare and biotechnology, and a variety of other settings. In many of these applications, the main goal is not to precisely estimate a treatment effect, but to demonstrate…

Sample quantiles, such as the median, are often better suited than the sample mean for summarising location characteristics of a data set. Similarly, linear combinations of sample quantiles and ratios of such linear combinations, e.g. the…

We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a (non-private)…

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…