Subdivision treats the syptoms, not the cause. The source of the problem is the terminator artifact ray biasing, which can be adjusted or even turned off:
The geometry offset defaults to .1, turn it to zero to negate this artifact.
If you start running into shadow terminator artifacts, then you will need to find a happy medium, but I generally find that I rarely ran into issues with those artifacts. I generally avoid high contrast small light sources and low poly smooth shaded models, but, as always, YMMV.