  Machine learning is rapidly becoming an integral part of experimental
physical discovery via automated and high-throughput synthesis, and active
experiments in scattering and electron/probe microscopy. This, in turn,
necessitates the development of active learning methods capable of exploring
relevant parameter spaces with the smallest number of steps. Here we introduce
an active learning approach based on co-navigation of the hypothesis and
experimental spaces. This is realized by combining the structured Gaussian
Processes containing probabilistic models of the possible system's behaviors
(hypotheses) with reinforcement learning policy refinement (discovery). This
approach closely resembles classical human-driven physical discovery, when
several alternative hypotheses realized via models with adjustable parameters
are tested during an experiment. We demonstrate this approach for exploring
concentration-induced phase transitions in combinatorial libraries of Sm-doped
BiFeO3 using Piezoresponse Force Microscopy, but it is straightforward to
extend it to higher-dimensional parameter spaces and more complex physical
problems once the experimental workflow and hypothesis-generation are
available.
