  Careful tuning of the learning rate, or even schedules thereof, can be
crucial to effective neural net training. There has been much recent interest
in gradient-based meta-optimization, where one tunes hyperparameters, or even
learns an optimizer, in order to minimize the expected loss when the training
procedure is unrolled. But because the training procedure must be unrolled
thousands of times, the meta-objective must be defined with an
orders-of-magnitude shorter time horizon than is typical for neural net
training. We show that such short-horizon meta-objectives cause a serious bias
towards small step sizes, an effect we term short-horizon bias. We introduce a
toy problem, a noisy quadratic cost function, on which we analyze short-horizon
bias by deriving and comparing the optimal schedules for short and long time
horizons. We then run meta-optimization experiments (both offline and online)
on standard benchmark datasets, showing that meta-optimization chooses too
small a learning rate by multiple orders of magnitude, even when run with a
moderately long time horizon (100 steps) typical of work in the area. We
believe short-horizon bias is a fundamental problem that needs to be addressed
if meta-optimization is to scale to practical neural net training regimes.
