Turbulent diffusion causes particles placed in proximity to separate. We investigate the required swimming efforts to maintain an active particle close to its passively advected counterpart. We explore optimally balancing these efforts by developing a novel physics-informed reinforcement learning strategy and comparing it with prescribed control and physics-agnostic reinforcement learning strategies. Our scheme, coined the actor-physicist, is an adaptation of the actor-critic algorithm in which the neural network parameterized critic is replaced with an analytically derived physical heuristic function, the physicist. We validate the proposed physics-informed reinforcement learning approach through extensive numerical experiments in both synthetic BK and more realistic Arnold-Beltrami-Childress flow environments, demonstrating its superiority in controlling particle dynamics when compared to standard reinforcement learning methods.