Both of these sentences are correct, and they carry same meaning. Depending on the setting, however, one may be preferred over the other, and which one that is will change, again, depending on the setting.

'I saw both the actors yesterday' sounds correct in spoken language and is colloquially fine but not perfect and I personally would say 'I saw both of the actors yesterday', this is more grammatically correct and sounds better. However there is also nothing wrong with 'I saw both actors yesterday'. In any of these phrases it is assumed that the two actors have already been mentioned, so the article can be used or can be left out. I think that 'I saw both of the actors yesterday' has slightly more emphasis on the 'both' element of the sentence.

Thanks Sajit.

I suppose b is correct. "I saw both the actors yesterday" sounds a bit awkward to me.