Compost Heap

I am looking after a hampster and wondered if the sawdust+ bedding + food remains which I bag up when cleaning out the cage, could be put on the compost heap ( which is a black bin with a lid ) or might the waste food(dry) encourage rats?

Ive had hamsters, guinea pigs and rabbits and ive always put the stuff in the compost bin. Mix it well in with all the green compost. Never had any rats. I  have 3 cats which bring in plenty of mice that come from the lady next door who has chickens. Lennie is a good mouser and always leaves a bit for me to clear up. How kind.

Thanks Maud, will do as you suggest.