I am Sebastien Bubeck, researcher in the Theory Group at Microsoft Research. My main research interests lie in the mathematics of machine learning and sequential decision making. One of the simplest (yet surprisingly rich) problem in sequential decision making is the so-called multi-armed bandit. I have devoted a fair amount of my research to this problem (hence the title of the blog!). If you want to learn more about this topic you can check this book co-authored with Nicolò Cesa-Bianchi. A large fraction of the posts on this blog have been on optimization, and this has resulted in another short book “Convex Optimization: Algorithms and Complexity”.

This blog is about various topics that I find interesting, essentially in optimization, probability and statistics.

## By George Anescu February 9, 2017 - 5:26 am

Hi Sebastian,

Please have a look at my working paper on RG: https://www.researchgate.net/publication/313164189_A_fast_gradient_descent_algorithm_for_strictly_quasiconvex_functions. My algorithm represents a different approach to gradient descent and is very fast according to my tests. I need to do some more testing with real life high dimensional problems, maybe you can help me with it.

## By Alexandros Georgogiannis February 29, 2016 - 8:23 am

Dear Sebastien,

i cannot complete the proof of Theorem 3.7 p.270 in your convex optimization book.

Specially, i cannot find the induction mentioned about the recursion

\delta_{s+1} \leq \delta_s + \frac{1}{2\beta||x_1 - x^*||^2}\delta_{s+1}^2$ on p.271

Can you point me any hint (or reference)?

Thnx!

## By Geetha Chandrasekaran October 13, 2015 - 6:46 am

Dear Sebastian,

Your blog has really augments well to the material that I have on Optimization algorithms. Thanks a ton!

Geetha

## By Sebastian Bubeck « Pink Iguana May 4, 2015 - 7:56 am

[…] Sebastian Bubeck, I’m a bandit, here. […]

## By Paolo January 1, 2015 - 9:46 am

Dear Sebastien,

I am a first year student in Mathematics. Reading your blog, I found myself really interested in your work and I saw you were looking for an intern. Is there a chance your internship offer is open to a first year student?

Best Regards,

Paolo

## By Sebastien Bubeck January 1, 2015 - 5:18 pm

Hi Paolo,

at the moment I am mainly looking for students who already have a couple of preprints.

Best,

Sebastien

## By Eric T. Han September 17, 2014 - 11:22 pm

Hi Sebastien,

I'm a PhD student in statistics and beginner for Bandit-related problems.

I was wondering that in order to get involved in this fruitful field, besides your basic bandit monograph, should I also go through your two published optimization lecture notes (intro.to online optimization & theory of convex optimization) ? Any suggestions to beginners?

Thanks a lot!

Best,

Eric

## By Sebastien Bubeck September 25, 2014 - 11:05 pm

Hi Eric,

the bandit monograph contains most of what you should know to start doing research on bandit-related problems. The two other set of lecture notes are useful to place bandit problems within the broader context of optimization and online learning. Obviously there are many other useful references besides these ones, but it's probably a good idea to first try to master the bandit monograph.

## By Christian JEANGUILLAUME August 5, 2013 - 1:06 pm

Dear Sebastian,

as you seems to know more than I in optimisation, have you ever hear about the optimisation in the non negative orthant (R+) that is a cone programming

with an objective function like xtQx+...

with a Q not positive definite, but as we are in the non negative orthant all the product xtQx>=0 . I mean an objective function positive semidefinite not by the fact of the matrix Q but by the choice of a special convex domain.

I would be interested by a solver able to solve such problem.

Thank you for the eventual interest you have on this.

Best regards

Christian

## By Sebastien Bubeck July 29, 2013 - 4:09 pm

Hi Dana,

I don't have a pdf for the moment. I will reorganize the course and add material next Spring and I plan to release a much more polished course in pdf around May 2014. Sorry for the long delay!

Seb

## By DANA MARINCA July 29, 2013 - 10:14 am

Hi,

I'm interested on the content of your course "The complexities of optimization". Would be possible to have a pdf version?

Thank you very much

Dana