Time-Uniform Self-Normalized Concentration for Discounted Least Squares: Limits and Corrections
Self-normalized concentration inequalities are standard tools in bandit and reinforcement-learning analyses. A widely used weighted extension claims an analogous time-uniform guarantee for discounted least-squares estimators in non-stationary problems. A simple scalar Gaussian counterexample with a fixed parameter shows that the claimed bounded radius is crossed with probability one. For fixed discount and regularization parameters, we further show that, when $δ\leq1/2$ and $T/δ$ is sufficiently large, any deterministic anytime boundary valid uniformly over the stated conditionally sub-Gaussian model class must be at least of order $R\sqrt{\log(T/δ)}$ at some time by horizon $T$; for nond...
| Authors | Yi-Shan Wu |
|---|---|
| Primary category | cs.LG |
| Published | 20 August 2026 |
| Last updated at source | 20 August 2026 |
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