等报酬动态随机背包问题中的对数后悔
Logarithmic regret in the dynamic and stochastic knapsack problem with equal rewards
摘要：
我们研究了一个动态的和随机的背包问题，其中的决策者顺序提出的项目到达根据伯努利过程在$n$离散时间段。项目具有从已知的非负连续分布$F$中得出的相等奖励和独立权重。决策者寻求最大化的预期总回报的项目，她包括在背包中，同时满足容量约束，而终端的决定，只要每个项目的重量是揭示。在温和的规则性条件下的权重分布$F$，我们证明了遗憾-最好的顺序算法的性能和先知谁看到所有的重量之前，作出任何决定的预期差异-是，最多，对数在$n$。我们的证据是有建设性的。我们设计了一个重新优化的启发式，实现这个遗憾的界限。
英文摘要：
We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with items arriving according to a Bernoulli process over $n$ discrete time periods. Items have equal rewards and independent weights that are drawn from a known non-negative continuous distribution $F$. The decision maker seeks to maximize the expected total reward of the items that she includes in the knapsack while satisfying a capacity constraint and while making terminal decisions as soon as each item weight is revealed. Under mild regularity conditions on the weight distribution $F$, we prove that the regret---the expected difference between the performance of the best sequential algorithm and that of a prophet who sees all of the weights before making any decision---is, at most, logarithmic in $n$. Our proof is constructive. We devise a reoptimized heuristic that achieves this regret bound.
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。
