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We study the convergence rate of the famous Symmetric Rank-1 (SR1) algorithmwhich has wide applications in different scenarios. Although it has beenextensively investigated, SR1 still lacks a non-asymptotic superlinear ratecompared with other quasi-Newton methods such as DFP and BFGS. In this paper weaddress this problem. Inspired by the recent work on explicit convergenceanalysis of quasi-Newton methods, we obtain the first explicit non-asymptoticrates of superlinear convergence for the vanilla SR1 methods with correctionstrategy to achieve the numerical stability. Specifically, the vanilla SR1 withthe correction strategy achieves the rates of the form$\left(\frac{4n\ln(e\kappa) }{k}\right)^{k/2}$ for general smoothstrongly-convex functions where $k$ is the iteration counter, $\kappa$ is thecondition number of the objective function and $n$ is the dimension of theproblem. For the quadratic function, the vanilla SR1 algorithm can find theoptima of the objective function at most $n$ steps.

Explicit Superlinear Convergence Rates of The SR1 Algorithm