Alpha lipoic acid and smell recovery?

Alpha lipoic acid was mentioned by Andrew Huberman as an over-the-counter remedy that can potentially accelerate the recovery of smell. He shared on the Huberman Lab that he took alpha lipoic acid and it worked successfully for him after experiencing olfactory loss due to COVID. However, it was also pointed out by Dr. Noam Sobel that it's uncertain if the recovery was due to the supplement or if it would have happened anyway since no control experiment was conducted 1. In the same discussion, olfactory training was noted to have strong evidence for success in smell recovery, which involves smelling various items attentively and consistently 2.