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A multitenant database management system (DBMS) in the cloud must continuously monitor the trade-off between efficient resource sharing among multiple application databases (tenants) and their performance. Considering the scale of \attn{hundreds to} thousands of tenants in such multitenant DBMSs, manual approaches for continuous monitoring are not tenable. A self-managing controller of a multitenant DBMS faces several challenges. For instance, how to characterize a tenant given its variety of workloads, how to reduce the impact of tenant colocation, and how to detect and mitigate a performance crisis where one or more tenants' desired service level objective (SLO) is not achieved. We present Delphi, a self-managing system controller for a multitenant DBMS, and Pythia, a technique to learn behavior through observation and supervision using DBMS-agnostic database level performance measures. Pythia accurately learns tenant behavior even when multiple tenants share a database process, learns good and bad tenant consolidation plans (or packings), and maintains a pertenant history to detect behavior changes. Delphi detects performance crises, and leverages Pythia to suggests remedial actions using a hill-climbing search algorithm to identify a new tenant placement strategy to mitigate violating SLOs. Our evaluation using a variety of tenant types and workloads shows that Pythia can learn a tenant's behavior with more than 92% accuracy and learn the quality of packings with more than 86% accuracy. During a performance crisis, Delphi is able to reduce 99th percentile latencies by 80%, and can consolidate 45% more tenants than a greedy baseline, which balances tenant load without modeling tenant behavior.