Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e.,~guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized ad recommendation in online marketing. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called {\em conservative linear UCB} (CLUCB), that simultaneously minimizes its regret and satisfies the safety constraint, i.e.,~maintains its performance above a fixed percentage of the performance of a baseline strategy, uniformly over time. We prove an upper-bound on the regret of CLUCB and show that it can be decomposed into two terms: {\bf 1)} an upper-bound for the regret of the standard linear UCB algorithm that grows with the time horizon and {\bf 2)} a constant (does not grow with the time horizon) term that accounts for the loss of being conservative in order to satisfy the safety constraint. We empirically show that our algorithm is safe and validate our theoretical analysis.

研究在基于上下文的线性多臂赌博机问题中的安全问题，提出了Conservative Linear UCB (CLUCB)算法，保证了安全性的同时，最小化了它的遗憾，并将其维持在一个固定的性能百分比之上。

保守上下文线性赌博机