Sublinear Least-Squares Value Iteration via Locality Sensitive Hashing

TL;DR

This paper introduces a novel sublinear runtime Least-Squares Value Iteration algorithm using Locality Sensitive Hashing, achieving significant efficiency improvements while maintaining regret bounds in reinforcement learning.

Contribution

It is the first to combine LSH with reinforcement learning for sublinear action complexity in value iteration algorithms.

Findings

Achieves sublinear runtime in the number of actions.

Maintains the same regret bounds as traditional LSVI algorithms.

First to integrate LSH with reinforcement learning for provable efficiency gains.

Abstract

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 STOC'98, Andoni and Razenshteyn STOC'15, Andoni, Laarhoven, Razenshteyn and Waingarten SODA'17] 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.