The young leaves look like they have fungal problems or sunburn. Not sure about the big leaves. Have you cut back on watering to see what happens? You may want to start spraying with some kind of fungicide as well. Quit feeding them until next spring. Does this begonia defoliate in winter? If so then it may be perfectly normal and there is nothing you can do other than let it rest. My 'Benitochiba', 'Selph's Mahogany', some other large sprawling rhizomatous NOID all defoliate in winter. I move them to the garage (very cool and not much light) and water sparingly every two weeks or more. They come back beautifully the next spring.

Butch

It looks to me like fungal problems on both leaves. I would cut out diseased parts and treat with a fungicide.

Thanks everybody for suggestions! I cut out damaged leaves and sprayed by fungiside. I hope it will help.