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This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in F.E. Curtis, K. Scheinberg, and R. Shi, A stochastic trust region algorithm based on careful step normalization, INFORMS. J. Optim. 1(3) (2019), pp. 200–220; F.E. Curtis and R. Shi, A fully stochastic second-order trust region method, Optim. Methods Softw. 37(3) (2022), pp. 844–877. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in R. Bollapragada, R. Byrd, and J. Nocedal, Adaptive sampling strategies for stochastic optimization, SIAM. J. Optim. 28(4) (2018), pp. 3312–3343. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.
Bellavia et al. (Thu,) studied this question.