Time-Uniform Self-Normalized Concentration for Discounted Least Squares: Limits and Corrections
It is shown that, when $\delta\leq1/2$ and $T/\delta$ is sufficiently large, any deterministic anytime boundary valid uniformly over the stated conditionally sub-Gaussian model class must be at least of order at some time by horizon $T$; for nondecreasing boundaries, this order is required at time $T$.