学习扮演强盗：多拟阵半强盗
Learning to Act Greedily: Polymatroid Semi-Bandits
摘要：
许多重要的优化问题，如最小生成树、最小费用流等，都可以用贪心法来求解。在这项工作中，我们研究了这些问题的学习变体，其中问题的模型是未知的，并且必须通过在强盗设置中与环境反复交互来学习。我们形式化我们的学习问题相当普遍，学习如何最大化一个未知的模函数在一个已知的polymatroid。我们提出了一个计算效率高的算法来解决我们的问题，并限制其预期的累积遗憾。我们的间隙依赖的上限是紧到一个常数，我们的间隙自由的上限是紧到多对数因子。最后，我们评估我们的方法上的三个问题，并证明它是实用的。
英文摘要：
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.
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。
