Related papers: Top Two Algorithms Revisited
In this paper we consider the problem of best-arm identification in multi-armed bandits in the fixed confidence setting, where the goal is to identify, with probability $1-\delta$ for some $\delta>0$, the arm with the highest mean reward in…
We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the…
A challenging aspect of the bandit problem is that a stochastic reward is observed only for the chosen arm and the rewards of other arms remain missing. The dependence of the arm choice on the past context and reward pairs compounds the…
The expected improvement (EI) algorithm is a popular strategy for information collection in optimization under uncertainty. The algorithm is widely known to be too greedy, but nevertheless enjoys wide use due to its simplicity and ability…
We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call…
Large language models (LLMs) have been adopted to solve sequential decision-making tasks such as multi-armed bandits (MAB), in which an LLM is directly instructed to select the arms to pull in every iteration. However, this paradigm of…
Given a set of arms $\mathcal{Z}\subset \mathbb{R}^d$ and an unknown parameter vector $\theta_\ast\in\mathbb{R}^d$, the pure exploration linear bandit problem aims to return $\arg\max_{z\in \mathcal{Z}} z^{\top}\theta_{\ast}$, with high…
The 1-identification problem is a fundamental pure-exploration problem in multi-armed bandits. An agent aims to determine whether there exists an arm whose mean reward exceeds a known threshold $\mu_0$, or to output \textsf{None} otherwise.…
Motivated by applications such as online labor markets we consider a variant of the stochastic multi-armed bandit problem where we have a collection of arms representing strategic agents with different performance characteristics. The…
This note describes the optimal policy rule, according to the local asymptotic minimax regret criterion, for best arm identification when there are only two treatments. It is shown that the optimal sampling rule is the Neyman allocation,…
We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design. Theorem 1 of Kasy and Sautmann (2021) provides three…
In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…
Fixed-budget best-arm identification (BAI) is a bandit problem where the agent maximizes the probability of identifying the optimal arm within a fixed budget of observations. In this work, we study this problem in the Bayesian setting. We…
In this paper, we introduce a multi-armed bandit problem termed max-min grouped bandits, in which the arms are arranged in possibly-overlapping groups, and the goal is to find the group whose worst arm has the highest mean reward. This…
We study the use of policy gradient algorithms to optimize over a class of generalized Thompson sampling policies. Our central insight is to view the posterior parameter sampled by Thompson sampling as a kind of pseudo-action. Policy…
Many algorithms for data analysis exist, especially for classification problems. To solve a data analysis problem, a proper algorithm should be chosen, and also its hyperparameters should be selected. In this paper, we present a new method…
We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how…
The stochastic multi-arm bandit problem has been extensively studied under standard assumptions on the arm's distribution (e.g bounded with known support, exponential family, etc). These assumptions are suitable for many real-world problems…
We consider the fixed-confidence best arm identification (FC-BAI) problem in the Bayesian setting. This problem aims to find the arm of the largest mean with a fixed confidence level when the bandit model has been sampled from the known…
We study a posterior sampling approach to efficient exploration in constrained reinforcement learning. Alternatively to existing algorithms, we propose two simple algorithms that are more efficient statistically, simpler to implement and…