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  1. Service function chaining (SFC), consisting of a sequence of virtual network functions (VNFs) (i.e., firewalls and load balancers), is an effective service provision technique in modern data center networks. By requiring cloud user traffic to traverse the VNFs in order, SFC im- proves the security and performance of the cloud user applications. In this paper, we study how to place an SFC inside a data center to mini- mize the network traffic of the virtual machine (VM) communication. We take a cooperative multi-agent reinforcement learning approach, wherein multiple agents collaboratively figure out the traffic-efficient route for the VM communication. Underlying the SFC placement is a fundamental graph-theoretical prob- lem called the k-stroll problem. Given a weighted graph G(V, E), two nodes s, t ∈ V , and an integer k, the k-stroll problem is to find the shortest path from s to t that visits at least k other nodes in the graph. Our work is the first to take a multi-agent learning approach to solve k- stroll problem. We compare our learning algorithm with an optimal and exhaustive algorithm and an existing dynamic programming(DP)-based heuristic algorithm. We show that our learning algorithm, although lack- ing the complete knowledge ofmore »the network assumed by existing research, delivers comparable or even better VM communication time while taking two orders of magnitude of less execution time.« less