具有不稳定马尔可夫报酬的组合网络优化的在线学习
Online Learning for Combinatorial Network Optimization with Restless Markovian Rewards
摘要：
考虑边权重计算最优结构的组合网络优化算法形成了许多网络协议的基础。例子包括最短路径路由，最小生成树计算，最大加权匹配的二分图等，我们提出CLRMR，第一个在线学习算法，有效地解决了这些问题的随机版本的基础边权重变化为独立的马尔可夫链与未知的动态。一个在线学习算法的性能的特点是在遗憾，定义为一个适当定义的精灵之间的奖励，并通过给定的算法获得的累积差异。我们证明，相比一个精灵，知道马尔可夫转移矩阵，并在任何时候都使用单一的最佳结构，CLRMR产量遗憾，是多项式的边缘数和近对数的时间。
英文摘要：
Combinatorial network optimization algorithms that compute optimal structures taking into account edge weights form the foundation for many network protocols. Examples include shortest path routing, minimal spanning tree computation, maximum weighted matching on bipartite graphs, etc. We present CLRMR, the first online learning algorithm that efficiently solves the stochastic version of these problems where the underlying edge weights vary as independent Markov chains with unknown dynamics. The performance of an online learning algorithm is characterized in terms of regret, defined as the cumulative difference in rewards between a suitably-defined genie, and that obtained by the given algorithm. We prove that, compared to a genie that knows the Markov transition matrices and uses the single-best structure at all times, CLRMR yields regret that is polynomial in the number of edges and nearly-logarithmic in time.
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