Introduction
A constant learning rate is a compromise. Early in training you're far from a good solution, and big steps make fast progress. Late in training you're close, and big steps make you bounce around the minimum instead of settling into it. A learning-rate schedule changes the learning rate over time to get the best of both.
Think of parking a car. You drive at normal speed through the car park (large learning rate), slow down as you approach your space, and creep the last few centimetres (small learning rate). Trying to park at a constant 30 km/h, or crawling the whole way at 1 km/h, would both be bad.
Many modern schedules also start with a short warm-up: a few hundred steps where the learning rate rises from almost zero, like letting the engine warm up before pulling out.