Adaptive Quantization Preserves Fast Rates for TD Learning over Rate-Limited Channels

A paper submitted to arXiv on 9 November 2026 introduces Batched Adaptively Quantized TD (BAQ-TD), an algorithm that preserves the convergence rate of unquantized temporal-difference learning over rate-limited channels. The authors prove a high-probability finite-time error bound showing that transmitting O(d log(T)) bits over a horizon of length T suffices to achieve the order-optimal rate of Õ(1/T) for a d-dimensional value function parameter, which the paper calls an exponential improvement in communication complexity over prior work. The result targets policy evaluation with linear function approximation in reinforcement learning subject to communication constraints.

Computer Science Machine Learning Submitted on 9 Nov 2026 Title:Adaptive Quantization Preserves Fast Rates for TD Learning over Rate-Limited Channels View PDF http://arxiv.org/pdf/2611.12878v1 Abstract:Motivated by reinforcement learning subject to communication constraints, we study a policy evaluation problem with linear function approximation over a rate-limited channel. In our setup, an agent interacting with an unknown environment modeled as a Markov Decision Process transmits quantized estimates of a temporal-difference TD learning update direction to a server over a finite-capacity channel. Our goal is to investigate to what extent one can preserve the statistical convergence rates achievable when the channel has infinite capacity. To that end, we propose a new algorithm called Batched Adaptively Quantized TD BAQ-TD , which uses batching to reduce the variance of the transmitted information, and adaptive quantization to encode innovations. We prove a high-probability finite-time error bound for BAQ-TD, and show that, above a certain finite channel capacity, BAQ-TD preserves the convergence rate of unquantized TD up to logarithmic factors. Specifically, for a $d$-dimensional value function parameter, we establish that transmitting a total of $\mathcal{O} d \log T $ bits over a horizon of length $T$ suffices to achieve the order-optimal rate of $\tilde{\mathcal{O}} 1/T $, marking an exponential improvement in communication-complexity over prior work. Additional Features References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .