具有Levy支付过程的Bandit问题
Bandit problems with Levy payoff processes
摘要：
我们研究两个武装利维土匪在连续时间，其中有一个安全的手臂，产生一个恒定的回报s，和一个风险的手臂，可以是高或低的类型，这两种类型产生随机收益的利维过程。当臂为高时，Levy过程的期望值大于s，如果臂为低，则小于s。决策者（DM）必须在任何给定的时间t选择在时间间隔[t，t+dt）内分配给每个臂的资源的分数。我们证明了在适当的条件下的Levy过程，有一个唯一的最优策略，这是一个截止策略，我们提供了一个明确的公式的截止和最优收益，作为一个函数的数据的问题。我们还研究了DM在风险臂类型上具有不正确先验的情况，并且我们计算了DM使用对应于不正确先验的最优策略所获得的预期收益。此外，我们研究了结果的两个应用：（a）我们展示了如何在双臂Levy强盗问题中定价信息，以及（b）我们研究了在双臂强盗问题中谁的表现更好：一个乐观主义者分配给高的概率高于真实概率，或者一个悲观主义者分配给高的概率低于真实概率。
英文摘要：
We study two-armed Levy bandits in continuous-time, which have one safe arm that yields a constant payoff s, and one risky arm that can be either of type High or Low; both types yield stochastic payoffs generated by a Levy process. The expectation of the Levy process when the arm is High is greater than s, and lower than s if the arm is Low. The decision maker (DM) has to choose, at any given time t, the fraction of resource to be allocated to each arm over the time interval [t,t+dt). We show that under proper conditions on the Levy processes, there is a unique optimal strategy, which is a cut-off strategy, and we provide an explicit formula for the cut-off and the optimal payoff, as a function of the data of the problem. We also examine the case where the DM has incorrect prior over the type of the risky arm, and we calculate the expected payoff gained by a DM who plays the optimal strategy that corresponds to the incorrect prior. In addition, we study two applications of the results: (a) we show how to price information in two-armed Levy bandit problem, and (b) we investigate who fares better in two-armed bandit problems: an optimist who assigns to High a probability higher than the true probability, or a pessimist who assigns to High a probability lower than the true probability.
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。
