Streaming applications are becoming widespread across an extensive range of business domains as an increasing number of sources continuously produce data that need to be processed and analysed in real time. Modern businesses are aggressively using streaming data to generate valuable knowledge that can be used to automate processes, help decision-making, optimize resource usage, and ultimately generate revenue for the organization. Despite their increased adoption and tangible benefits, support for the automated deployment and management of streaming applications is yet to emerge. Although a plethora of stream management systems have flooded the open source community in recent years, all of the existing frameworks demand a considerably challenging and lengthy effort from human operators to manually and continuously tune their configuration and deployment environment in order to reach and maintain the desired performance goals. To address these challenges, this article proposes a vision for creating Deep Reinforcement Learning (DRL)-based methods for transforming stream processing engines into self-managed serverless solutions. This will lead to an increase in productivity as engineers can focus on the actual development process, an increase in application performance potentially leading to reduced response times and more accurate and meaningful results, and a considerable decrease in operational costs for organizations.