I see interveinal chlorosis on many of the leaves, so perhaps the browning is a late stage of chlorosis. In that case, the culprit might be a nutrient deficiency (nitrogen or magnesium, for example). Potted plants are especially susceptible to nutrient loss because whatever nutrients are there get flushed out by watering and rain. So I'd recommend fertilizing with a balanced fertilizer. Read here:
http://web.extension.illinois.edu/cfiv/homeowners/010616.html

Overwatering is also possible. So is sunburn (although sweet potato is tolerant of full sun).