[{_id:1,items:[{item_id:1,desc:[{desc_id:1,description:"Test entry"},{desc_id:2,description:"Test entry 2"}]}]}]

db.collection.update({"items.desc.desc_id":1},{$set:{"items.$.desc.$[item].description":"Other test entry"}},{arrayFilters:[{"item.desc_id":1}]})