Optimal and Adaptive Monteiro-Svaiter Acceleration

Understand

We develop a variant of the Monteiro-Svaiter (MS) acceleration framework that removes the need to solve an expensive implicit equation at every iteration.

• Consequently, for any $p\ge 2$ we improve the complexity of convex optimization with Lipschitz $p$th derivative by a logarithmic factor, matching a lower bound.
• We also introduce an MS subproblem solver that requires no knowledge of problem parameters, and implement it as either a second- or first-order method by solving linear systems or applying MinRes, respectively.
• On logistic regression our method outperforms previous second-order momentum methods, but under-performs Newton's method; simply iterating our first-order adaptive subproblem solver performs comparably to L-BFGS.