Nikita Doikov

Welcome!

I do research in Computational Mathematics with a focus on Numerical Optimization and Machine Learning.

Now I am a postdoctoral researcher at EPFL, Switzerland, working in the Machine Learning and Optimization Laboratory with Martin Jaggi.

I am excited to explore provably efficient optimization algorithms that exploit the problem structure and combine ideas from various fields. One of my areas of expertise is second-order methods and its global complexity bounds. I believe that bridging the gap between the second-order optimization theory and the best known computational practices is what can lead us to new achievements in the training process of our models.

I defended my PhD in 2021 at UCLouvain, Belgium, supervised by Yurii Nesterov. My thesis is "New second-order and tensor methods in Convex Optimization".

I received a BSc degree in Computational Mathematics and Cybernetics from Lomonosov Moscow State University in 2015. I obtained a MSc degree from Higher School of Economics in 2017, where I was studying advanced statistical and optimization methods.

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Papers

Preprints / Various

• First and zeroth-order implementations of the regularized Newton method with lazy approximated Hessians. Nikita Doikov and Geovani Nunes Grapiglia, 2023 (arXiv)
• Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method. Nikita Doikov, 2023 (arXiv)
• Lower Complexity Bounds for Minimizing Regularized Functions. Nikita Doikov, 2022 (arXiv)

Refereed Conference Publications

• Linearization Algorithms for Fully Composite Optimization. Maria-Luiza Vladarean, Nikita Doikov, Martin Jaggi, and Nicolas Flammarion, 2023 (COLT proceedings, arXiv)
• Polynomial Preconditioning for Gradient Methods. Nikita Doikov and Anton Rodomanov, 2023 (ICML proceedings, arXiv)
• Second-order optimization with lazy Hessians. Nikita Doikov, El Mahdi Chayti, and Martin Jaggi, 2023 (ICML proceedings, arXiv)
• Convex optimization based on global lower second-order models. Nikita Doikov and Yurii Nesterov, 2020 (NeurIPS proceedings, arXiv, code)
• Stochastic Subspace Cubic Newton Method. Filip Hanzely, Nikita Doikov, Peter Richtárik, and Yurii Nesterov, 2020 (ICML proceedings, arXiv)
• Inexact Tensor Methods with Dynamic Accuracies. Nikita Doikov and Yurii Nesterov, 2020 (ICML proceedings, arXiv, code)
• Randomized Block Cubic Newton Method. Nikita Doikov and Peter Richtárik, 2018 (ICML proceedings, arXiv)

Journal Publications

• Super-Universal Regularized Newton Method. Nikita Doikov, Konstantin Mishchenko, and Yurii Nesterov, 2023 (to appear in SIOPT journal, arXiv, code)
• Gradient Regularization of Newton Method with Bregman Distances. Nikita Doikov and Yurii Nesterov, 2023 (Math. Program. journal, arXiv)
• High-Order Optimization Methods for Fully Composite Problems. Nikita Doikov and Yurii Nesterov, 2022 (SIOPT journal, arXiv)
• Affine-invariant contracting-point methods for Convex Optimization. Nikita Doikov and Yurii Nesterov, 2022 (Math. Program. journal, arXiv, code)
• Local convergence of tensor methods. Nikita Doikov and Yurii Nesterov, 2021 (Math. Program. journal, arXiv)
• Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method. Nikita Doikov and Yurii Nesterov, 2021 (JOTA journal, arXiv)
• Contracting Proximal Methods for Smooth Convex Optimization. Nikita Doikov and Yurii Nesterov, 2020 (SIOPT journal, arXiv)

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Recent Talks

• August 25, 2023: Super-Universal Regularized Newton Method, EUROPT, Budapest (slides)
• July 20, 2023: Second-Order Optimization with Lazy Hessians, ICML, Hawaii (slides, poster) [photo↓]
• July 19, 2023: Polynomial Preconditioning for Gradient Methods, ICML, Hawaii (poster)
• June 3, 2023: Second-Order Optimization with Lazy Hessians, SIAM Conference on Optimization, Seattle (slides) [photo↓]
• September 27, 2022: Super-Universal Regularized Newton Method, TML Laboratory, EPFL (slides)
• July 29, 2022: Affine-invariant contracting-point methods for Convex Optimization, EUROPT, Lisbon (slides)
• June 3, 2022: Second-order methods with global convergence in Convex Optimization, the research team of Panos Patrinos, KULeuven (slides)
• May 5, 2022: Optimization Methods for Fully Composite Problems, FGP-22, Porto (slides)
• February 21, 2022: Second-order methods with global convergence in Convex Optimization, MLO Laboratory, EPFL (slides)
• July 7, 2021: Local convergence of tensor methods, EUROPT, online (slides)
• March 4, 2021: Affine-invariant contracting-point methods for Convex Optimization, Symposium on Numerical Analysis and Optimization (invited by Geovani Nunes Grapiglia), UFPR, online (slides)
• October 28, 2020: Convex optimization based on global lower second-order models, NeurIPS, online (slides, poster)
• June 17, 2020: Inexact Tensor Methods with Dynamic Accuracies, ICML, online (slides, poster, video)
• October 8, 2019: Proximal Method with Contractions for Smooth Convex Optimization, ICTEAM seminar, Louvain-la-Neuve
• September 23, 2019: Proximal Method with Contractions for Smooth Convex Optimization, Optimization and Learning for Data Science seminar (invited by Dmitry Grishchenko) Université Grenoble Alpes, Grenoble (slides) [photo↓]
• September 18, 2019: Complexity of Cubically Regularized Newton Method for Minimizing Uniformly Convex Functions, FGS-19, Nice (slides)
• August 5, 2019: Complexity of Cubically Regularized Newton Method for Minimizing Uniformly Convex Functions, ICCOPT, Berlin
• July 5, 2019: Randomized Block Cubic Newton Method, Summer School on Optimization, Big Data and Applications, Veroli [photo↓]
• June 28, 2019: Complexity of Cubically Regularized Newton Method for Minimizing Uniformly Convex Functions EUROPT, Glasgow [photo↓]
• June 20, 2018: Randomized Block Cubic Newton Method, ICML, Stockholm (slides, poster, video) [photo↓]
• June 13, 2018: Randomized Block Cubic Newton Method, X Traditional summer school on Optimization, Voronovo [photo↓]

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