RESEARCH

Limiting Extrapolation in Linear Approximate Value Iteration

November 03, 2020

Abstract

We study linear approximate value iteration (LAVI) with a generative model. While linear models may accurately represent the optimal value function using a few parameters, several empirical and theoretical studies show the combination of least-squares projection with the Bellman operator may be expansive, thus leading LAVI to amplify errors over iterations and eventually diverge. We introduce an algorithm that approximates value functions by combining Q-values estimated at a set of \textit{anchor} states. Our algorithm tries to balance the generalization and compactness of linear methods with the small amplification of errors typical of interpolation methods. We prove that if the features at any state can be represented as a convex combination of features at the anchor points, then errors are propagated linearly over iterations (instead of exponentially) and our method achieves a polynomial sample complexity bound in the horizon and the number of anchor points. These findings are confirmed in preliminary simulations in a number of simple problems where a traditional least-square LAVI method diverges.

Download the Paper

AUTHORS

Written by

Alessandro Lazaric

Andrea Zanette

Emma Brunskill

Mykel Kochenderfer

Publisher

NeurIPS

Related Publications

June 27, 2025

HUMAN & MACHINE INTELLIGENCE

CONVERSATIONAL AI

Seamless Interaction: Dyadic Audiovisual Motion Modeling and Large-Scale Dataset

Vasu Agrawal, Akinniyi Akinyemi, Kathryn Alvero, Morteza Behrooz, Julia Buffalini, Fabio Maria Carlucci, Joy Chen, Junming Chen, Zhang Chen, Shiyang Cheng, Praveen Chowdary, Joe Chuang, Antony D'Avirro, Jon Daly, Ning Dong, Mark Duppenthaler, Cynthia Gao, Jeff Girard, Martin Gleize, Sahir Gomez, Hongyu Gong, Srivathsan Govindarajan, Brandon Han, Sen He, Denise Hernandez, Yordan Hristov, Rongjie Huang, Hirofumi Inaguma, Somya Jain, Raj Janardhan, Qingyao Jia, Christopher Klaiber, Dejan Kovachev, Moneish Kumar, Hang Li, Yilei Li, Pavel Litvin, Wei Liu, Guangyao Ma, Jing Ma, Martin Ma, Xutai Ma, Lucas Mantovani, Sagar Miglani, Sreyas Mohan, Louis-Philippe Morency, Evonne Ng, Kam-Woh Ng, Tu Anh Nguyen, Amia Oberai, Benjamin Peloquin, Juan Pino, Jovan Popovic, Omid Poursaeed, Fabian Prada, Alice Rakotoarison, Alexander Richard, Christophe Ropers, Safiyyah Saleem, Vasu Sharma, Alex Shcherbyna, Jie Shen, Anastasis Stathopoulos, Anna Sun, Paden Tomasello, Tuan Tran, Arina Turkatenko, Bo Wan, Chao Wang, Jeff Wang, Mary Williamson, Carleigh Wood, Tao Xiang, Yilin Yang, Zhiyuan Yao, Chen Zhang, Jiemin Zhang, Xinyue Zhang, Jason Zheng, Pavlo Zhyzheria, Jan Zikes, Michael Zollhoefer