Search Results for author: Mark Sellke

Found 11 papers, 0 papers with code

The Pareto Frontier of Instance-Dependent Guarantees in Multi-Player Multi-Armed Bandits with no Communication

no code implementations19 Feb 2022 Allen Liu, Mark Sellke

We ask whether it is possible to obtain optimal instance-dependent regret $\tilde{O}(1/\Delta)$ where $\Delta$ is the gap between the $m$-th and $m+1$-st best arms.

Multi-Armed Bandits

Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments

no code implementations18 Jun 2021 Yining Chen, Elan Rosenfeld, Mark Sellke, Tengyu Ma, Andrej Risteski

Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments.

Domain Generalization

A Universal Law of Robustness via Isoperimetry

no code implementations NeurIPS 2021 Sébastien Bubeck, Mark Sellke

Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied.

Metric Transforms and Low Rank Matrices via Representation Theory of the Real Hyperrectangle

no code implementations23 Nov 2020 Josh Alman, Timothy Chu, Gary Miller, Shyam Narayanan, Mark Sellke, Zhao Song

This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.

Algorithmic pure states for the negative spherical perceptron

no code implementations29 Oct 2020 Ahmed El Alaoui, Mark Sellke

In this paper we design an efficient algorithm which, given oracle access to the solution of the Parisi variational principle, exploits this conjectured FRSB structure for $\kappa<0$ and outputs a vector $\hat{\sigma}$ satisfying $\langle g_a , \hat{\sigma}\rangle \ge \kappa \sqrt{N}$ for all $1\le a \le M$ and lying on a sphere of non-trivial radius $\sqrt{\bar{q} N}$, where $\bar{q} \in (0, 1)$ is the right-end of the support of the associated Parisi measure.

Probability Data Structures and Algorithms Mathematical Physics Mathematical Physics

Online Multiserver Convex Chasing and Optimization

no code implementations15 Apr 2020 Sébastien Bubeck, Yuval Rabani, Mark Sellke

We introduce the problem of $k$-chasing of convex functions, a simultaneous generalization of both the famous k-server problem in $R^d$, and of the problem of chasing convex bodies and functions.

The Price of Incentivizing Exploration: A Characterization via Thompson Sampling and Sample Complexity

no code implementations3 Feb 2020 Mark Sellke, Aleksandrs Slivkins

The performance loss due to incentives is therefore limited to the initial rounds when these data points are collected.

Multi-Armed Bandits

First-Order Bayesian Regret Analysis of Thompson Sampling

no code implementations2 Feb 2019 Sébastien Bubeck, Mark Sellke

Second we replace the entropy over combinatorial actions by a coordinate entropy, which allows us to obtain the first optimal worst-case bound for Thompson Sampling in the combinatorial setting.

Combinatorial Optimization

Approximating Continuous Functions by ReLU Nets of Minimal Width

no code implementations31 Oct 2017 Boris Hanin, Mark Sellke

Specifically, we answer the following question: for a fixed $d_{in}\geq 1,$ what is the minimal width $w$ so that neural nets with ReLU activations, input dimension $d_{in}$, hidden layer widths at most $w,$ and arbitrary depth can approximate any continuous, real-valued function of $d_{in}$ variables arbitrarily well?

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