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- W3136019718 abstract "Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives. However, its remarkable empirical success is not fully explained by this optimality, as the worst-case analysis -- contrary to the average-case -- is not representative of the expected complexity of an algorithm. In this work we establish a novel link between PM and the average-case analysis. Our main contribution is to prove that any optimal average-case method converges in the number of iterations to PM, under mild assumptions. This brings a new perspective on this classical method, showing that PM is asymptotically both worst-case and average-case optimal." @default.
- W3136019718 created "2021-03-29" @default.
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- W3136019718 date "2020-11-21" @default.
- W3136019718 modified "2023-09-26" @default.
- W3136019718 title "Universal Average-Case Optimality of Polyak Momentum" @default.
- W3136019718 hasPublicationYear "2020" @default.
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