We establish a global finite-sample guarantee for synchronous quantile temporal-difference learning (QTD) in tabular distributional reinforcement learning. The proof separates two stability mechanisms. A global comparison argument, based on the order monotonicity of reward cumulative distribution functions and the $W_\infty$ contraction of the distributional Bellman operator, brings an arbitrarily initialized iterate into a local neighborhood. Inside that neighborhood, we linearize the QTD mean field. Its Jacobian is a nonsingular $M$-matrix, and the associated positive semigroup permits a variance-sensitive martingale analysis. For stepsizes $\alpha_t=c(t+1)^{-a}$ with $a\in(1/2,1)$, the leading last-iterate fluctuation is of order $\widetilde O\bigl(T^{-a/2}/\sqrt{1-\gamma}\bigr)$ and has no polynomial dependence on the number of quantiles. The deterministic transient and the required burn-in can still depend on the smallest Bellman-target density, which is of order $m^{-1}$ in the worst case. The result therefore distinguishes sharply between the local stochastic fluctuation and the global sample complexity.
A local asymptotic theory is developed for the estimated return CDF over $T^{-1/2}$-neighborhoods of finitely many thresholds, together with its bootstrap analogue that justifies bootstrap inference for smooth statistical functionals, including variance, CVaR, expected shortfall, and expectiles.
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 $T$.
We study the stochastic differential equation $$d X_t=b(t,X_t)d t+\sqrt{2}d W_t$$ on $\mathbb R^d$, where $b$ is a time-dependent, divergence-free distributional drift of critical H\"older--Besov regularity $-1$, strengthened by an iterated-logarithmic correction. For every initial probability law, we construct a weak...
A Brownian-bridge self-normalizer yields asymptotically pivotal confidence regions for prespecified state-value contrasts for prespecified state-value contrasts without estimating the long-run covariance or selecting a bandwidth or batch length.
This paper studies online quantile regression for large-scale and streaming data using Stochastic SubGradient Descent (SSGD) with constant learning rates. Classical offline inference for quantile regression is computationally and memory intensive. Existing works of online inference for quantile regression provide only...
Zi-Yang Wei, Jia-Qi Li, Lan Wang et al.· 0 citations
Adaptive algorithms increasingly make decisions while reshaping the dynamics that generate their future data. We establish a shrinking-tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain. The bound guarantees, with high probability, that every iterate after a chosen time r...
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
