arXiv:2608. 12973v3 Announce Type: replace-cross Abstract: In this paper, we study online statistical inference for quantile-based distributional policy evaluation, which aims to characterize the distribution of discounted cumulative rewards under a given policy.
arXiv:2605. 26000v2 Announce Type: replace-cross Abstract: Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization.
arXiv:2609. 13040v1 Announce Type: new Abstract: We study loss-based filtering for finite-sum optimization with a subset of corrupted component functions whose gradients may be highly unreliable.
arXiv:2608. 08204v1 Announce Type: cross Abstract: This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation.
arXiv:2606. 28652v1 Announce Type: cross Abstract: Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity.
This paper studies the statistical properties of Stochastic Gradient Descent (SGD) with a constant step size using the framework of iterated random functions. It demonstrates convergence in Euclidean distance via Geometric Moment Contraction, establishes quenched central limit theorems, invariance principles, and α-stable convergence for averaged SGD regardless of initialization, and explores the effect of step sizes through derivative processes. The authors further develop a Richardson-Romberg extrapolation with multiple step sizes, propose a bias-reduced variant, and introduce an online inference method that yields empirical confidence intervals with coverage approaching nominal levels as sample size increases.
arXiv:2607. 08444v1 Announce Type: cross Abstract: In this paper, we study quantile-based distributional reinforcement learning from the perspective of statistical efficiency.
arXiv:2608. 27313v2 Announce Type: replace-cross Abstract: Quantile temporal-difference learning (QTD) is an effective method for learning return distributions through quantile approximation, yet its finite-time behavior remains poorly understood.
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
arXiv:2607. 26577v1 Announce Type: new Abstract: Adaptive conformal inference (ACI) of Gibbs and Cand{\`e}s and its variants are the standard approach to online conformal prediction under distribution shift, but they suffer from three fundamental limitations.
arXiv:2608. 14408v1 Announce Type: cross Abstract: We study online statistical inference for functionals of the return distribution under a fixed policy.
arXiv:2606. 00265v1 Announce Type: cross Abstract: We study quantile regression in an extrapolation regime where the covariate takes unusually large values.