Computer Science > Machine Learning
Title: Adaptive Quantization Preserves Fast Rates for TD Learning over Rate-Limited Channels
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.
Submission history
Access Paper:
Additional Features
Current browse context:
References & Citations
BibTeX formatted citation
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
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 .