Despite advancements in MLOps and AutoML, ML development still remains challenging for data scientists. First, there is poor support for and limited control over optimizing and evolving ML models. Second, there is lack of efficient mechanisms for continuous evolution of ML models which would leverage the knowledge gained in previous optimizations of the same or different models. We propose an experiment-driven MLOps approach which tackles these problems. Our approach relies on the concept of an experiment, which embodies a fully controllable optimization process. It introduces full traceability and repeatability to the optimization process, allows humans to be in full control of it, and enables continuous improvement of the ML system. Importantly, it also establishes knowledge, which is carried over and built across a series of experiments and allows for improving the efficiency of experimentation over time. We demonstrate our approach through its realization and application in the ExtremeXP1 project (Horizon Europe).