Constructing Optimal Optimization Methods using BnB-PEP

07/28/2023, 3:40 PM3:50 PM UTC


We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal optimization method as a nonconvex but practically tractable quadratically constrained quadratic optimization problem and solves it to certifiable global optimality using a customized branch-and-bound algorithm.


By directly confronting the nonconvexity, BnB-PEP offers significantly more flexibility and removes the many limitations of the prior methodologies. Our customized branch-and-bound algorithm, through exploiting specific problem structures, outperforms the latest off-the-shelf implementations by orders of magnitude, accelerating the solution time from hours to seconds and weeks to minutes. Finally, we apply BnB-PEP to several setups for which the prior methodologies do not apply and obtain methods with bounds that improve upon prior state-of-the-art results. Open source Julia implementation of BnB-PEP is available at:

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Pumas AIQuEra Computing Inc.Relational AIJeffrey Sarnoff

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Jolin.ioBeacon BiosignalsMIT CSAILBoeing

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