IEEE Transactions on Signal Processing最新文献

英文中文

Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification 方差-最优臂选择：错配最小化和最佳臂识别

IF 5.8 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Signal Processing

Pub Date : 2026-02-23 DOI: 10.1109/TSP.2026.3666223

Sabrina Khurshid;Gourab Ghatak;Mohammed Shahid Abdulla

This paper focuses on selecting the arm with the highest variance from a set of

$ K $

independent arms. Specifically, we focus on two settings: (i) misallocation minimization setting, that penalizes the number of pulls of suboptimal arms in terms of variance, and (ii) fixed-budget best arm identification setting, that evaluates the ability of an algorithm to determine the arm with the highest variance after a fixed number of pulls. We develop a novel online algorithm called UCB-VV for the misallocation minimization (MM) and show that its upper bound on misallocation for bounded rewards evolves as

$mathcal{O}left(log{n}right)$

where

$ n $

is the horizon. By deriving the lower bound on the misallocation, we show that UCB-VV is order optimal. For the fixed budget best arm identification (BAI) setting we propose the SHVV algorithm. We show that the upper bound of the error probability of SHVV evolves as

$expleft(-frac{n}{log(K)H}right)$

, where

$ H $

represents the complexity of the problem, and this rate matches the corresponding lower bound. We extend the framework from bounded distributions to sub-Gaussian distributions using a novel concentration inequality on the sample variance and standard deviation. Leveraging the same, we derive a concentration inequality for the empirical Sharpe ratio (SR) for sub-Gaussian distributions, which was previously unknown in the literature. Empirical simulations show that UCB-VV consistently outperforms

$epsilon$

-greedy across different sub-optimality gaps though it is surpassed by VTS, which exhibits the lowest misallocation, albeit lacking in theoretical guarantees. We also illustrate the superior performance of SHVV, for a fixed budget setting under 6 different setups against uniform sampling. Finally, we conduct a case study to empirically evaluate the performance of the UCB-VV and SHVV in call option trading on 100 stocks generated using geometric Brownian motion (GBM).

本文的重点是从一组$ K $独立臂中选择方差最大的臂。具体来说，我们关注两种设置：(i)错配最小化设置，即在方差方面惩罚次优手臂的拉拔次数，以及（ii）固定预算最佳手臂识别设置，即评估算法在固定次数拉拔后确定方差最大的手臂的能力。我们开发了一种新的在线算法，称为UCB-VV，用于最小化错误分配（MM），并证明其在有限奖励下错误分配的上界演变为$mathcal{O}left(log{n}right)$，其中$ n $为视界。通过推导错配的下界，我们证明了UCB-VV是阶最优的。对于固定预算最优臂识别（BAI）设置，我们提出了SHVV算法。我们表明，SHVV的错误概率的上界演变为$expleft(-frac{n}{log(K)H}right)$，其中$ H $表示问题的复杂性，并且该比率与相应的下界匹配。我们使用一个新的样本方差和标准差的集中不等式将框架从有界分布扩展到亚高斯分布。利用同样的方法，我们得出了亚高斯分布的经验夏普比率（SR）的集中不等式，这在以前的文献中是未知的。实证模拟表明，UCB-VV在不同的次最优性差距上始终优于$epsilon$ -greedy，尽管它被VTS超越，后者表现出最低的错配，尽管缺乏理论保证。我们还说明了SHVV在6种不同采样设置下的固定预算设置的优越性能。最后，我们进行了一个案例研究，实证评估了UCB-VV和SHVV在使用几何布朗运动（GBM）生成的100只股票看涨期权交易中的表现。

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