ABSTRACT Feedback from active galactic nuclei (AGNs) and supernovae can affect measurements of integrated Sunyaev–Zeldovich (SZ) flux of haloes (YSZ) from cosmic microwave background (CMB) surveys, and cause its relation with the halo mass (YSZ–M) to deviate from the self-similar power-law prediction of the virial theorem. We perform a comprehensive study of such deviations using CAMELS, a suite of hydrodynamic simulations with extensive variations in feedback prescriptions. We use a combination of two machine learning tools (random forest and symbolic regression) to search for analogues of the Y–M relation which are more robust to feedback processes for low masses ($M\lesssim 10^{14}\, \mathrm{ h}^{-1} \, \mathrm{ M}_\odot$); we find that simply replacing Y → Y(1 + M*/Mgas) in the relation makes it remarkably self-similar. This could serve as a robust multiwavelength mass proxy for low-mass clusters and galaxy groups. Our methodology can also be generally useful to improve the domain of validity of other astrophysical scaling relations. We also forecast that measurements of the Y–M relation could provide per cent level constraints on certain combinations of feedback parameters and/or rule out a major part of the parameter space of supernova and AGN feedback models used in current state-of-the-art hydrodynamic simulations. Our results can be useful for using upcoming SZ surveys (e.g. SO, CMB-S4) and galaxy surveys (e.g. DESI and Rubin) to constrain the nature of baryonic feedback. Finally, we find that the alternative relation, Y–M*, provides complementary information on feedback than Y–M.