什么时候双臂强盗算法可以被信任？
When can the two-armed bandit algorithm be trusted?
摘要：
我们调查的一个版本的所谓的双臂强盗算法的渐近行为。它是随机逼近过程的一个例子，其相关的常微分方程具有排斥和吸引平衡，在该平衡点上该过程是无噪声的。我们表明，如果增益参数是恒定的或去0不太快，该算法确实落在无噪声的排斥平衡与正概率，而它总是收敛到其自然的吸引力的目标时，增益参数去0在一些适当的速率取决于模型的参数。我们还阐明了当步长为0时，常数步长算法的行为。最后，我们强调的算法和波利亚瓮之间的连接。资产配置的应用程序进行了简要说明。
英文摘要：
We investigate the asymptotic behavior of one version of the so-called two-armed bandit algorithm. It is an example of stochastic approximation procedure whose associated ODE has both a repulsive and an attractive equilibrium, at which the procedure is noiseless. We show that if the gain parameter is constant or goes to 0 not too fast, the algorithm does fall in the noiseless repulsive equilibrium with positive probability, whereas it always converges to its natural attractive target when the gain parameter goes to zero at some appropriate rates depending on the parameters of the model. We also elucidate the behavior of the constant step algorithm when the step goes to 0. Finally, we highlight the connection between the algorithm and the Polya urn. An application to asset allocation is briefly described.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
