Sublinear Least-Squares Value Iteration via Locality Sensitive Hashing
arXiv:2105.08285
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.
References in corpus (14)
- Deep Reinforcement Learning for Dialogue Generation
- Provably Efficient Reinforcement Learning with Linear Function Approximation
- Practical and Optimal LSH for Angular Distance
- Powers of Tensors and Fast Matrix Multiplication
- Faster Dynamic Matrix Inverse for Faster LPs
- Quantization based Fast Inner Product Search
- Learning Space Partitions for Nearest Neighbor Search
- Norm-Ranging LSH for Maximum Inner Product Search
- Efficient Model-free Reinforcement Learning in Metric Spaces
- Accelerating SLIDE Deep Learning on Modern CPUs: Vectorization, Quantizations, Memory Optimizations, and More
- A Provably Efficient Algorithm for Linear Markov Decision Process with Low Switching Cost
- Lsh-sampling Breaks the Computation Chicken-and-egg Loop in Adaptive Stochastic Gradient Estimation
- Climbing the WOL: Training for Cheaper Inference
- Linear Bandit Algorithms with Sublinear Time Complexity