Abstract
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally accelerated coordinate descent method that achieves the efficient algorithmic complexity of iteration and allows taking advantage of the data sparseness. It was considered an example of applying the proposed approach to optimizing a SoftMax-like function, for which the described method allowing weaken the dependence of the computational complexity on the dimension n in \(\mathcal {O}(\sqrt{n})\) times and, in practice, demonstrates a faster convergence in comparison with standard methods. As an example of applying the proposed approach, it was shown a variant of obtaining on its basis some efficient methods for optimizing Markov Decision Processes (MDP) in a minimax formulation with a Nesterov smoothed target function.
D.A. Pasechnyuk’s research was supported by the A.M. Raigorodsky Scholarship in the field of optimization and RFBR grant 19-31-51001 (Scientific mentoring). The work of V.V. Matyukhin was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment) No. 075-00337-20-03, project number 0714-2020-0005.
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Notes
- 1.
For the detailed proofs see appendices in full paper version on https://arxiv.org/abs/2103.06688.
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Pasechnyuk, D., Matyukhin, V. (2021). On the Computational Efficiency of Catalyst Accelerated Coordinate Descent. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_12
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