#### BSc at Moscow Institute of Physics and Technology

Department of Control and Applied Mathematics

Thesis: Accelerated Directional Searchs and Gradient-Free Methods with non-Euclidean prox-structure

I am a first year student of MS program at Moscow Institute of Physics and Technology, Department of Control and Applied Mathematics. I work under supervision of professor Alexander Gasnikov. My research interests include Stochastic Optimization and its applications to Machine Learning.

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My e-mail: ed-gorbunov at yandex dot ru

- Operating systems: Microsoft Windows, Linux, Mac OSX
- Programming languages: Python, LaTeX, C, C++

- Russian (native)
- English (fluent)

- Football: 9 years in football school in Rybinsk, Russia. Now I am playing for an amateur team and a student team.
- Table tennis, fitness

Sep 2014 - Jun 2018

Department of Control and Applied Mathematics

Thesis: Accelerated Directional Searchs and Gradient-Free Methods with non-Euclidean prox-structure

Sep 2018 - Present

Department of Control and Applied Mathematics

**[05 September, 2018]**

The paper "Stochastic spectral and conjugate descent methods" - joint work with Dmitry Kovalev, Elnur Gasanov and Peter Richtárik - accepted to The Thirty-second Annual Conference on Neural Information Processing Systems (NIPS).

Abstract:*The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.*

The conference will be in Montreal, Canada during December 3-8, 2018.

---------------------------------------------------------**[01 July - 06 July, 2018]**

I am attending the 23rd International Symposium on Mathematical Programming in Bordeaux, France. My talk is scheduled on Friday, 06 July, in the section*"New methods for stochastic optimization and variational inequalities".*

The Talk:*”An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization”*

[slides]

---------------------------------------------------------**[27 June - 28 June, 2018]**

I am in Grenoble, attending the Grenoble Optimization Days 2018. By the way I have the new most favorite photo!

Here I read the excellent book by my advisor Alexander Gasnikov.

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**[25 June, 2018]**

Today I successfully defended my Bachelor diploma.

Thesis: "Accelerated Directional Searchs and Gradient-Free Methods with non-Euclidean prox-structure"

---------------------------------------------------------**[10 June - 15 June, 2018]**

I am in Traditional Youth School ”Control, Information and Optimization” (Voronovo, Russia) organized by Boris Polyak and Elena Gryazina.

I presented a poster*"An Accelerated Directional Derivative Method for SmoothStochastic Convex Optimization".*My work was chosen and I gave a talk there. I won third prize for this talk in competitions of best talks among participants.

[slides of the talk]

---------------------------------------------------------**[14 April, 2018]**

I am attending workshop*”Optimization at Work”*at MIPT (Moscow, Russia) with a talk*”An Accelerated Method for Derivative-Free Smooth Stochastic Convex Optimization”*.

[slides] [video]

---------------------------------------------------------**[10 April, 2018]****New paper out:**"On the upper bound for the mathematical expectation of the norm of a vector uniformly distributed on the sphere and the phenomenon of concentration of uniform measure on the sphere" - joint work with Evgeniya Vorontsova and Alexander Gasnikov.

Abstract:*We considered the problem of obtaining upper bounds for the mathematical expectation of the q-norm (2⩽q⩽∞) of the vector which is uniformly distributed on the unit Euclidean sphere.*

---------------------------------------------------------**[8 April, 2018]**An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization" - joint work with Pavel Dvurechensky and Alexander Gasnikov.

New paper out: "

Abstract:*We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the directional derivative of the objective function at this point and in this direction is available with some additive noise. The noise is assumed to be of an unknown nature, but bounded in the absolute value. We underline that we consider directional derivatives in any direction, as opposed to coordinate descent methods which use only derivatives in coordinate directions. For this setting, we propose a non-accelerated and an accelerated directional derivative method and provide their complexity bounds. Despite that our algorithms do not use gradient information, our non-accelerated algorithm has a complexity bound which is, up to a factor logarithmic in problem dimension, similar to the complexity bound of gradient-based algorithms. Our accelerated algorithm has a complexity bound which coincides with the complexity bound of the accelerated gradient-based algorithm up to a factor of square root of the problem dimension, whereas for existing directional derivative methods this factor is of the order of problem dimension. We also extend these results to strongly convex problems. Finally, we consider derivative-free optimization as a particular case of directional derivative optimization with noise in the directional derivative and obtain complexity bounds for non-accelerated and accelerated derivative-free methods. Complexity bounds for these algorithms inherit the gain in the dimension dependent factors from our directional derivative methods.*

---------------------------------------------------------**[25 February, 2018]****New paper out:**"An Accelerated Method for Derivative-Free Smooth Stochastic Convex Optimization" - joint work with Pavel Dvurechensky and Alexander Gasnikov.

Abstract:*We consider an unconstrained problem of minimization of a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is of a stochastic nature. On the opposite, the second part is an additive noise of an unknown nature, but bounded in the absolute value. In the two-point feedback setting, i.e. when pairs of function values are available, we propose an accelerated derivative-free algorithm together with its complexity analysis. The complexity bound of our derivative-free algorithm is only by a factor of \sqrt{n} larger than the bound for accelerated gradient-based algorithms, where n is the dimension of the decision variable. We also propose a non-accelerated derivative-free algorithm with a complexity bound similar to the stochastic-gradient-based algorithm, that is, our bound does not have any dimension-dependent factor. Interestingly, if the solution of the problem is sparse, for both our algorithms, we obtain better complexity bound if the algorithm uses a 1-norm proximal setup, rather than the Euclidean proximal setup, which is a standard choice for unconstrained problems.*

---------------------------------------------------------**[10 February, 2018]****New paper out**: "Stochastic spectral and conjugate descent methods" - joint work with Dmitry Kovalev, Elnur Gasanov and Peter Richtárik.

Abstract:*The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.*

---------------------------------------------------------**[9 February, 2018]**

I started my final semester as a Bachelor student today. This spring I will be a tutor for the course "Algorithms and Models of Computation".

---------------------------------------------------------**[5 February - 7 February, 2018]**

I am attending KAUST Research Workshop on Optimization and Big Data with poster*”Stochastic Spectral Descent Methods”*based on our joint work with Dmitry Kovalev, Elnur Gasanov and Peter Richtárik.

---------------------------------------------------------**[14 January - 08 February, 2018]**

I am visiting Peter Richtárik at KAUST.

---------------------------------------------------------**[25 November, 2017]**Today I got a prize for the best talk in Section of Information Transmission Problems, Data Analysis and Optimization, 60th Scientific Conference of MIPT.

The talk:*”About accelerated Directional Search with non-Euclidean prox-structure”*

[slides]

---------------------------------------------------------**[27 October, 2017]**

I am attending workshop ”Optimization at Work” at MIPT (Moscow, Russia) with a talk*”Accelerated Directional Search with non-Euclidean prox-structure”.*[slides]*---------------------------------------------------------***[30 September, 2017]****New paper out:**"Accelerated Directional Search with non-Euclidean prox-structure" - joint work with Evgeniya Vorontsova and Alexander Gasnikov.

Abstract:*In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstrained optimization problem in R^n. For simplicity we start from the zero point. We expect in advance that 1-norm of the solution is close enough to its 2-norm. In this case the standard accelerated Nesterov's directional search method can be improved. In the paper we show how to make Nesterov's method n-times faster (up to a log n-factor) in this case. The basic idea is to use linear coupling, proposed by Allen-Zhu & Orecchia in 2014, and to make Grad-step in 2-norm, but Mirr-step in 1-norm. We show that for constrained optimization problem this approach stable upon an obstacle.*

---------------------------------------------------------**[29 July, 2017]**I am happy to announce that I started working with Peter Richtárik as a member of his research group at MIPT.