Machine learning assisted directed evolution often involves experimentally collecting data from a relatively small number of variants to update a surrogate model, due to experimental limitations of characterisation and sequencing at high throughput. We propose an alternative approach, involving collecting high-throughput experimental data in a manner that results in a large number of characterised variants at the cost of reduced information: although the sequences and the measured fitness values are known, their correspondence is not. In particular we explore applying this method to the optimisation of a recently discovered phenomenon: magnetically sensitive fluorescent proteins.