This note discusses proofs of convergence for gradient methods (also called “first-order methods”) based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants. We hope the structure and presentation of these amortized-analysis proofs will be useful as a guiding principle in learning and using these proofs.

Additional Metadata
Keywords Convex optimization, Potential function, Amortized analysis
Persistent URL dx.doi.org/10.4086/toc.2019.v015a004
Journal Theory of Computing
Citation
Bansal, N, & Gupta, A. (2019). Potential-function proofs for gradient methods. Theory of Computing, 15. doi:10.4086/toc.2019.v015a004