Streaming Linear System Identification with Reverse Experience Replay

by   Prateek Jain, et al.

We consider the problem of estimating a stochastic linear time-invariant (LTI) dynamical system from a single trajectory via streaming algorithms. The problem is equivalent to estimating the parameters of vector auto-regressive (VAR) models encountered in time series analysis (Hamilton (2020)). A recent sequence of papers (Faradonbeh et al., 2018; Simchowitz et al., 2018; Sarkar and Rakhlin, 2019) show that ordinary least squares (OLS) regression can be used to provide optimal finite time estimator for the problem. However, such techniques apply for offline setting where the optimal solution of OLS is available apriori. But, in many problems of interest as encountered in reinforcement learning (RL), it is important to estimate the parameters on the go using gradient oracle. This task is challenging since standard methods like SGD might not perform well when using stochastic gradients from correlated data points (Györfi and Walk, 1996; Nagaraj et al., 2020). In this work, we propose a novel algorithm, SGD with Reverse Experience Replay (SGD-RER), that is inspired by the experience replay (ER) technique popular in the RL literature (Lin, 1992). SGD-RER divides data into small buffers and runs SGD backwards on the data stored in the individual buffers. We show that this algorithm exactly deconstructs the dependency structure and obtains information theoretically optimal guarantees for both parameter error and prediction error for standard problem settings. Thus, we provide the first - to the best of our knowledge - optimal SGD-style algorithm for the classical problem of linear system identification aka VAR model estimation. Our work demonstrates that knowledge of dependency structure can aid us in designing algorithms which can deconstruct the dependencies between samples optimally in an online fashion.



page 1

page 2

page 3

page 4


Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems

We consider the setting of vector valued non-linear dynamical systems X_...

Online Target Q-learning with Reverse Experience Replay: Efficiently finding the Optimal Policy for Linear MDPs

Q-learning is a popular Reinforcement Learning (RL) algorithm which is w...

Look Back When Surprised: Stabilizing Reverse Experience Replay for Neural Approximation

Experience replay methods, which are an essential part of reinforcement ...

Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms

We study the problem of least squares linear regression where the data-p...

Learning from Censored and Dependent Data: The case of Linear Dynamics

Observations from dynamical systems often exhibit irregularities, such a...

Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectory

This work investigates the problem of estimating the weight matrices of ...

A Robotic Model of Hippocampal Reverse Replay for Reinforcement Learning

Hippocampal reverse replay is thought to contribute to learning, and par...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.