To navigate in spatial fields of sensory cues, bacterial cells employ gradient sensing by temporal comparison for run-and-tumble chemotaxis. Sensing and motility noise imply trade-off choices between precision and accuracy. To gain insight into these trade-offs, we learn optimal chemotactic decision filters using supervised machine learning, applying support vector machines to a biologically motivated training dataset. We discuss how the optimal filter depends on the level of sensing and motility noise, and derive an empirical power law for the optimal measurement time with as a function of the rotational diffusion coefficient D _rot characterizing motility noise. A weak amount of motility noise slightly increases chemotactic performance.