2020
I’m a bandit
by Sebastien Bubeck
3y ago
My latest post on this blog was on December 30th 2019. It seems like a lifetime away. The rate at which paradigm shifting events have been happening in 2020 is staggering. And it might very well be that the worst of 2020 is ahead of us, especially for those of us currently in the USA. When I started communicating online broadly (blog, twitter) I promised myself to keep it strictly about science (or very closely neighboring topics), so the few lines above is all I will say about the current worldwide situation. In other news, as is evident from the 10 months hiatus in blogging, I have taken els ..read more
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A decade of fun and learning
I’m a bandit
by Sebastien Bubeck
4y ago
I started out this decade with the project of writing a survey of the multi-armed bandit literature, which I had read thoroughly during the graduate studies that I was about to finish. At the time we resisted the temptation to name the survey “modern banditology”, which was indeed the right call given how much this “modern” picture has evolved over the decade! It is truly wonderful to now end the decade with two new iterations on the work we did in that survey: Bandit algorithms by Tor Lattimore and Csaba Szepesvari Introduction to bandits by Alex Slivkins These new references very signific ..read more
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Convex body chasing, Steiner point, Sellke point, and SODA 2020 best papers
I’m a bandit
by Sebastien Bubeck
4y ago
Big congratulations to my former intern Mark Sellke, and to the CMU team (C. J. Argue, Anupam Gupta, Guru Guruganesh, and Ziye Tang) for jointly winning the best paper award at SODA 2020 (as well as the best student paper for Mark)! They obtain a linear in the dimension competitive ratio for convex body chasing, a problem which was entirely open for any just two years ago. What’s more is that they found the algorithm (and proof) from The Book! Let me explain.   Convex body chasing In convex body chasing an online algorithm is presented at each time step with a convex body , and it must choose ..read more
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Guest post by Julien Mairal: A Kernel Point of View on Convolutional Neural Networks, part II
I’m a bandit
by Sebastien Bubeck
5y ago
This is a continuation of Julien Mairal‘s guest post on CNNs, see part I here. Stability to deformations of convolutional neural networks In their ICML paper Zhang et al. introduce a functional space for CNNs with one layer, by noticing that for some dot-product kernels, smoothed variants of rectified linear unit activation functions (ReLU) live in the corresponding RKHS, see also this paper and that one. By following a similar reasoning with multiple layers, it is then possible to show that the functional space described in part I contains CNNs with such smoothed ReLU, and that the norm of ..read more
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Guest post by Julien Mairal: A Kernel Point of View on Convolutional Neural Networks, part I
I’m a bandit
by Sebastien Bubeck
5y ago
I (n.b., Julien Mairal) have been interested in drawing links between neural networks and kernel methods for some time, and I am grateful to Sebastien for giving me the opportunity to say a few words about it on his blog. My initial motivation was not to provide another “why deep learning works” theory, but simply to encode into kernel methods a few successful principles from convolutional neural networks (CNNs), such as the ability to model the local stationarity of natural images at multiple scales—we may call that modeling receptive fields—along with feature compositions and invariant rep ..read more
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Optimal bound for stochastic bandits with corruption
I’m a bandit
by Sebastien Bubeck
5y ago
Guest post by Mark Sellke. In the of the previous blog post we asked if the new viewpoint on best of both worlds can be used to get clean “interpolation” results. The context is as follows: in a STOC 2018 paper followed by a COLT 2019 paper, the following corruption model was discussed: stochastic bandits, except for rounds which are adversarial. The state of the art bounds were of the form: optimal (or almost optimal) stochastic term plus , and it was mentioned as an open problem whether could be improved to (there is a lower bound showing that is necessary — when ). As was discussed in ..read more
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Amazing progress in adversarially robust stochastic multi-armed bandits
I’m a bandit
by Sebastien Bubeck
5y ago
In this post I briefly discuss some recent stunning progress on robust bandits (for more background on bandits see these two posts, part 1 and part 2, in particular what is described below gives a solution to Open Problem 3 at the end of part 2). Stochastic bandit and adversarial examples In multi-armed bandit problems the gold standard property, going back to a seminal paper of Lai and Robbins in 1985 is to have a regret upper bounded by: (1)   Let me unpack this a bit: this is for the scenario where the reward process for each action is simply an i.i.d. sequence from some fixed distribut ..read more
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