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We present the first provable Least-Squares Value Iteration (LSVI) algorithms that have runtime complexity sublinear in the number of actions. We formulate the value function estimation procedure in value iteration as an approximate maximum inner product search problem and propose a locality sensitive hashing (LSH) [Indyk and Motwani STOC98, Andoni and Razenshteyn STOC15, Andoni, Laarhoven, Razenshteyn and Waingarten SODA17] type data structure to solve this problem with sublinear time complexity. Moreover, we build the connections between the theory of approximate maximum inner product search and the regret analysis of reinforcement learning. We prove that, with our choice of approximation factor, our Sublinear LSVI algorithms maintain the same regret as the original LSVI algorithms while reducing the runtime complexity to sublinear in the number of actions. To the best of our knowledge, this is the first work that combines LSH with reinforcement learning resulting in provable improvements. We hope that our novel way of combining data-structures and iterative algorithm will open the door for further study into cost reduction in optimization.
Locality Sensitive Hashing (LSH) is an effective method of indexing a set of items to support efficient nearest neighbors queries in high-dimensional spaces. The basic idea of LSH is that similar items should produce hash collisions with higher proba
Extended differential privacy, a generalization of standard differential privacy (DP) using a general metric, has been widely studied to provide rigorous privacy guarantees while keeping high utility. However, existing works on extended DP are limite
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained in recent w
Metagenomic binning is an essential task in analyzing metagenomic sequence datasets. To analyze structure or function of microbial communities from environmental samples, metagenomic sequence fragments are assigned to their taxonomic origins. Althoug
We give a new approach to the dictionary learning (also known as sparse coding) problem of recovering an unknown $ntimes m$ matrix $A$ (for $m geq n$) from examples of the form [ y = Ax + e, ] where $x$ is a random vector in $mathbb R^m$ with at most