  If the trend of learned components eventually outperforming their
hand-crafted version continues, learned optimizers will eventually outperform
hand-crafted optimizers like SGD or Adam. Even if learned optimizers (L2Os)
eventually outpace hand-crafted ones in practice however, they are still not
provably convergent and might fail out of distribution. These are the questions
addressed here. Currently, learned optimizers frequently outperform generic
hand-crafted optimizers (such as gradient descent) at the beginning of learning
but they generally plateau after some time while the generic algorithms
continue to make progress and often overtake the learned algorithm as Aesop's
tortoise which overtakes the hare. L2Os also still have a difficult time
generalizing out of distribution. Heaton et al. proposed Safeguarded L2O (GL2O)
which can take a learned optimizer and safeguard it with a generic learning
algorithm so that by conditionally switching between the two, the resulting
algorithm is provably convergent. We propose a new class of Safeguarded L2O,
called Loss-Guarded L2O (LGL2O), which is both conceptually simpler and
computationally less expensive. The guarding mechanism decides solely based on
the expected future loss value of both optimizers. Furthermore, we show
theoretical proof of LGL2O's convergence guarantee and empirical results
comparing to GL2O and other baselines showing that it combines the best of both
L2O and SGD and that in practice converges much better than GL2O.
