Synthetic active matter systems, such as active colloids, often have complex interactions, which can be of hydrodynamic, chemical or electrostatic origin and cannot be computed from first principles. Here, we use stochastic force inference to learn general pair interactions, including transverse forces and torques, between self-propelled Janus particles from experimental trajectories. We use data from two experiments: one where the particles flock, and one where the system remains disordered. The learned interactions are then fed to numerical simulations, which reproduce all the experimental observables and could be extrapolated to different densities. Overall, we find that the radial interaction is mostly repulsive and isotropic, while the angular interaction has a richer angular dependence, which controls the behavior of the system; the transverse interaction is negligible. Finally, testing the symmetry relations obeyed by the inferred interactions allows us to show that they cannot come from electrostatics only, so that they must have a hydrodynamic component.
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