In recent years, applications of cloud services have been increasingly expanded. Cloud services, are distributed infrastructures which develop the communication and services. Auto scaling is one of the most important features of cloud services which dedicates and retakes the allocated dynamic resource in proportion to the volume of requests. Scaling tries to utilize maximum power of the available resources also to use idle resources, in order to maximize the efficiency or shut down unnecessary resources to reduce the cost of running requests. In this paper, we have suggested an approach based on learning automata auto- scaling, in order to manage and optimize factors like cost, rate of violations of user-level agreements (SLA Violation) as well as stability in the presence of traffic workload. Results of simulation show that proposed approach has been able to optimize cost and rate of SLA violation in order to manage their trade off. Also, it decreases number of operation needed for scaling to increase stability of system compared to the other approaches.