Ultrafast laser systems, such as optical parametric chirped pulse amplifiers (OPCPA), are complex tools. Optimizing laser performance for a given application is often plagued by intricate couplings between different output parameters, making simultaneous control of multiple pulse properties difficult. Here, we experimentally demonstrate an autonomous tuning procedure of a white-light seeded two-stage OPCPA using an evolutionary strategy to reliably reach an optimized working point. We use the data collected during the tuning procedure to calibrate a performance model of the laser system, which we then apply to stabilize the intricately coupled laser output energy and spectrum simultaneously. Our approach ensures reliable day-to-day operation at optimized working points without manual tuning. We demonstrate shot-to-shot energy stability of <0.18 % rms, in combination with <25 pm rms wavelength stability and <0.2 % rms bandwidth stability during multi-day operation.