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Spotlight Poster

Online Control for Meta-optimization

Xinyi Chen · Elad Hazan

Great Hall & Hall B1+B2 (level 1) #2023
[ ]
[ Paper [ Poster [ OpenReview
Wed 13 Dec 3 p.m. PST — 5 p.m. PST


Choosing the optimal hyperparameters, including learning rate and momentum, for specific optimization instances is a significant yet non-convex challenge. This makes conventional iterative techniques such as hypergradient descent \cite{baydin2017online} insufficient in obtaining global optimality guarantees.We consider the more general task of meta-optimization -- online learning of the best optimization algorithm given problem instances, and introduce a novel approach based on control theory. We show how meta-optimization can be formulated as an optimal control problem, departing from existing literature that use stability-based methods to study optimization. Our approach leverages convex relaxation techniques in the recently-proposed nonstochastic control framework to overcome the challenge of nonconvexity, and obtains regret guarantees vs. the best offline solution. This guarantees that in meta-optimization, we can learn a method that attains convergence comparable to that of the best optimization method in hindsight from a class of methods.

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