不确定世界中的路由：适应性，效率和均衡
Routing in an Uncertain World: Adaptivity, Efficiency, and Equilibrium
摘要：
我们考虑了非原子路由博弈中的交通分配问题，其中参与者的成本函数可能会受到随机波动的影响（例如，天气扰动、底层网络中的扰动等）。我们从控制接口的角度来解决这个问题，该控制接口仅根据观察到的成本进行路由建议，而不需要对系统的管理动态有任何进一步的了解-例如网络的成本函数，影响网络的任何随机事件的分布等。在这种在线设置中，基于流行的指数权重算法的学习方法以$\mathcal{O}({1/\sqrt{T}})$的速率收敛到平衡：已知该速率在随机网络中是阶最优的，但在静态网络中是次优的。在后一种情况下，可以通过使用微调的加速算法来实现$\mathcal{O}({1/T^{2}})$均衡收敛速度;另一方面，这些加速算法在存在持续随机性的情况下无法完全收敛，因此不清楚如何在收敛速度方面实现“两全其美”。本文提出了一种自适应路由算法$(i)$，它分别在静态和随机环境下无缝地插入$\mathcal{O}({1/T^{2}})$和$\mathcal{O}({1/\sqrt{T}})$速率之间，$(ii)$的收敛速度是网络中路径数的多对数; ${(iii)}$--该方法的每次迭代复杂度和内存需求都与网络中的节点和边的数量成线性关系;和${(iv)}$，它不需要问题参数的任何先验知识。
英文摘要：
We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this problem from the viewpoint of a control interface that makes routing recommendations based solely on observed costs and without any further knowledge of the system's governing dynamics -- such as the network's cost functions, the distribution of any random events affecting the network, etc. In this online setting, learning methods based on the popular exponential weights algorithm converge to equilibrium at an $\mathcal{O}({1/\sqrt{T}})$ rate: this rate is known to be order-optimal in stochastic networks, but it is otherwise suboptimal in static networks. In the latter case, it is possible to achieve an $\mathcal{O}({1/T^{2}})$ equilibrium convergence rate via the use of finely tuned accelerated algorithms; on the other hand, these accelerated algorithms fail to converge altogether in the presence of persistent randomness, so it is not clear how to achieve the "best of both worlds" in terms of convergence speed. Our paper seeks to fill this gap by proposing an adaptive routing algortihm with the following desirable properties: $(i)$ it seamlessly interpolates between the $\mathcal{O}({1/T^{2}})$ and $\mathcal{O}({1/\sqrt{T}})$ rates for static and stochastic environments respectively; $(ii)$ its convergence speed is polylogarithmic in the number of paths in the network; ${(iii)}$ the method's per-iteration complexity and memory requirements are both linear in the number of nodes and edges in the network; and ${(iv)}$ it does not require any prior knowledge of the problem's parameters.
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。
