A Single Stepsize Suffices for Unprojected Linear TD(0): Simultaneous Robust and Fast Rates via Polyak--Ruppert Averaging
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:A Single Stepsize Suffices for Unprojected Linear TD(0): Simultaneous Robust and Fast Rates via Polyak--Ruppert Averaging
Abstract:We study linear TD(0) under Markovian sampling, where data are generated along a single trajectory. We provide high-probability guarantees for a plain unprojected TD(0) algorithm with Polyak-Ruppert (PR) averaging, using a single stepsize schedule $\eta_t \propto \frac{1}{\tau_{\mathrm{mix}}\log(t)\sqrt{t}}$ that depends on the mixing time but requires no prior knowledge of the curvature parameter $\omega$. Our first result shows that such a choice of the stepsize guarantees that the TD(0) iterates are automatically and uniformly bounded with high probability, without projections and without any stability argument based on $\omega$. Building on this result, we establish a simultaneous high-probability convergence guarantee for the PR average: the same stepsize yields both a robust curvature-free $\widetilde{\mathcal{O}}\!\left(\frac{\tau_{\mathrm{mix}}}{\sqrt{T}}\right)$ rate and a fast curvature-dependent $\widetilde{\mathcal{O}}\!\left(\frac{\tau_{\mathrm{mix}}^2}{\omega T}\right)$rate, with the bound taking the minimum of the two. The core technical ingredient is a Poisson-equation toolkit for geometrically mixing Markov chains, which decomposes Markov noise into a martingale term plus a controlled remainder and enables a new self-bounding inductive argument for pathwise stability.
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML) |
| Cite as: | arXiv:2606.24981 [cs.LG] |
| (or arXiv:2606.24981v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.24981
arXiv-issued DOI via DataCite
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
Current browse context:
References & Citations
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.
More from arXiv — Machine Learning
-
Can AI Draw Science? A Benchmark for Evaluating Scientific Figure Generation by Text-to-Image and Multimodal Models
Jun 30
-
On the Necessity of a Liquid Substrate for Mesh Intelligence
Jun 30
-
Position: RL Researchers Need to Distinguish Between Solving Simulators and Using Simulators as a Proxy
Jun 30
-
Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter
Jun 30
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.