no code implementations • 22 Feb 2021 • Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena, Zhao Song, Huacheng Yu

In addition, we show a similar $\tilde{\Theta}(n \cdot \sqrt{L})$ bound on the space complexity of any algorithm (with any number of passes) for the related problem of sampling an $L$-step random walk from every vertex in the graph.

Data Structures and Algorithms Computational Complexity

no code implementations • 21 Sep 2020 • Lijie Chen, Badih Ghazi, Ravi Kumar, Pasin Manurangsi

We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(\epsilon, \delta)$-differentially privacy: - In the non-interactive local setting, we prove that the additive error of any protocol is $\Omega(n)$ for any constant $\epsilon$ and for any $\delta$ inverse polynomial in $n$.

no code implementations • 4 Jun 2017 • Lijie Chen, Anupam Gupta, Jian Li, Mingda Qiao, Ruosong Wang

We provide a novel instance-wise lower bound for the sample complexity of the problem, as well as a nontrivial sampling algorithm, matching the lower bound up to a factor of $\ln|\mathcal{F}|$.

no code implementations • 13 Feb 2017 • Lijie Chen, Jian Li, Mingda Qiao

In the Best-$k$-Arm problem, we are given $n$ stochastic bandit arms, each associated with an unknown reward distribution.

no code implementations • 22 Aug 2016 • Lijie Chen, Jian Li, Mingda Qiao

$H(I)=\sum_{i=2}^n\Delta_{[i]}^{-2}$ is the complexity of the instance.

no code implementations • 27 May 2016 • Lijie Chen, Jian Li

The best arm identification problem (BEST-1-ARM) is the most basic pure exploration problem in stochastic multi-armed bandits.

no code implementations • 23 May 2016 • Lijie Chen, Anupam Gupta, Jian Li

In a Best-Basis instance, we are given $n$ stochastic arms with unknown reward distributions, as well as a matroid $\mathcal{M}$ over the arms.

no code implementations • 12 Nov 2015 • Lijie Chen, Jian Li

The $i$th arm has a reward distribution $D_i$ with an unknown mean $\mu_{i}$.

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