[{"customerSchemes":[{"name":"A","startDate":2},{"name":"B","startDate":1}]},{"customerSchemes":[{"name":"A","startDate":1},{"name":"B","startDate":5}]},{"customerSchemes":[{"name":"A","startDate":4},{"name":"B","startDate":1}]}]

db.collection.aggregate([{"$addFields":{"fields":{"$reduce":{"input":"$customerSchemes","initialValue":{},"in":{"$mergeObjects":[{"$arrayToObject":[[["$$this.name","$$this.startDate"]]]},"$$value"]}}}}},{"$match":{"$expr":{"$gt":["$fields.A","$fields.B"]}}},{"$project":{"fields":0}}])