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Currently, there is a growing trend of outsourcing the execution of DNNs to cloud services. For service providers, managing multi-tenancy and ensuring high-quality service delivery, particularly in meeting stringent execution time constraints, assumes paramount importance, all while endeavoring to maintain cost-effectiveness. In this context, the utilization of heterogeneous multi-accelerator systems becomes increasingly relevant. This paper presents RELMAS, a low-overhead deep reinforcement learning algorithm designed for the online scheduling of DNNs in multi-tenant environments, taking into account the dataflow heterogeneity of accelerators and memory bandwidths contentions. By doing so, service providers can employ the most efficient scheduling policy for user requests, optimizing Service-Level-Agreement (SLA) satisfaction rates and enhancing hardware utilization. The application of RELMAS to a heterogeneous multi-accelerator system composed of various instances of Simba and Eyeriss sub-accelerators resulted in up to a 173% improvement in SLA satisfaction rate compared to state-of-the-art scheduling techniques across different workload scenarios, with less than a 1.5% energy overhead.