We consider the problem of efficiently routing jobs that arrive into a central queue to a system of heterogeneous servers. Unlike homogeneous systems, a threshold policy, that routes jobs to the slow server(s) when the queue length exceeds a certain threshold, is known to be optimal for the one-fast-one-slow two-server system. But an optimal policy for the multi-server system is unknown and non-trivial to find. While Reinforcement Learning (RL) has been recognized to have great potential for learning policies in such cases, our problem has an exponentially large state space size, rendering standard RL inefficient. In this work, we propose ACHQ, an efficient policy gradient based algorithm with a low dimensional soft threshold policy parameterization that leverages the underlying queueing structure. We provide stationary-point convergence guarantees for the general case and despite the low-dimensional parameterization prove that ACHQ converges to an approximate global optimum for the special case of two servers. Simulations demonstrate an improvement in expected response time of up to ~30% over the greedy policy that routes to the fastest available server.

翻译：我们考虑将到达中央队列的任务高效路由至异构服务器系统的问题。不同于同构系统，已知对于一快一慢双服务器系统，当队列长度超过某一阈值时将任务路由至慢服务器的最优策略是阈值策略。但对于多服务器系统，最优策略未知且求解难度极大。尽管强化学习在此类策略学习中具有巨大潜力，但本问题的状态空间规模呈指数级增长，导致标准强化学习方法效率低下。为此，我们提出ACHQ——一种基于策略梯度的高效算法，通过利用底层排队结构实现低维软阈值策略参数化。我们为一般情形提供了驻点收敛性保证，并证明尽管采用低维参数化，ACHQ在双服务器特例中仍能收敛至近似全局最优解。仿真结果表明，与路由至最快可用服务器的贪婪策略相比，期望响应时间最多可降低约30%。