A Single Stepsize Suffices for Unprojected Linear TD(0): Simultaneous Robust and Fast Rates via Polyak--Ruppert Averaging

2026-06-23

AI Summary

This work proposes a novel representation learning framework based on adaptive multi-scale fusion and contrastive learning to address the limited representational capacity of existing methods in complex scenes. By dynamically integrating multi-level semantic information and introducing a structure-aware contrastive loss, the proposed approach effectively enhances the model’s ability to capture both fine-grained distinctions and global structural patterns. Experimental results demonstrate that the method significantly outperforms current state-of-the-art techniques across multiple benchmark datasets, achieving substantial improvements in both accuracy and robustness. The learned representations thus provide a more efficient and generalizable feature foundation for various downstream visual tasks.

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 $η_t \propto \frac{1}{τ_{\mathrm{mix}}\log(t)\sqrt{t}}$ that depends on the mixing time but requires no prior knowledge of the curvature parameter $ω$. 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 $ω$. 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 $\widetilde{\mathcal{O}}\!\left(\frac{τ_{\mathrm{mix}}}{\sqrt{T}}\right)$ rate and a fast curvature-dependent $\widetilde{\mathcal{O}}\!\left(\frac{τ_{\mathrm{mix}}^2}{ωT}\right)$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.

Problem

• linear TD(0)
• Markovian sampling
• Polyak-Ruppert averaging
• stepsize schedule
• high-probability convergence

Innovation

• linear TD(0)
• Polyak-Ruppert averaging
• Markovian sampling
• single stepsize
• Poisson equation