---
title: "Frequency-Uniform Log-Regret Reinforcement Learning for Diffusions"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.36758v1"
permalink: "https://feed.astralor.com/items/itm_72df10b9e550e8bf909876a3"
published: "2026-10-27T07:14:35.000Z"
score: 55
channel: "ai"
tags: ["LLM","Frequency-Uniform Log-Regret Reinforcement","Learning","Diffusions High-frequency","High-frequency","Euler","Under"]
---

# Frequency-Uniform Log-Regret Reinforcement Learning for Diffusions

## 速览

High-frequency control problems are often studied through time discretization, but refining the timestep $δ$ increases the discrete horizon $H=T/δ$ and can make standard finite-horizon regret guarantees deteriorate even…

## 关键点

- High-frequency control problems are often studied through time discretization, but refining the timestep $δ$ increases the discrete horizon $H=T/δ$ and can make standard finite-horizon regret guarantees deteriorate even…
- We study episodic value-based reinforcement learning for Euler discretizations of controlled diffusions.
- The performance is measured as the cumulative regret over $K$ episodes relative to the optimal policy of the corresponding Euler model.

## 全文

High-frequency control problems are often studied through time discretization, but refining the timestep $δ$ increases the discrete horizon $H=T/δ$ and can make standard finite-horizon regret guarantees deteriorate even when the physical horizon $T$ is fixed. We study episodic value-based reinforcement learning for Euler discretizations of controlled diffusions. The performance is measured as the cumulative regret over $K$ episodes relative to the optimal policy of the corresponding Euler model. Under stability and regularity conditions on value function gradients, Bellman residual derivatives, and fitted critics, we prove an $\mathcal{O}(\log K)$ regret bound with constants uniform in $δ$. For dynamics with drift linear in unknown parameters and unknown constant diffusion covariance, we verify localized versions of these conditions for a constrained, model-based controlled-diffusion fitted-$Q$ algorithm (CD-FQ) and obtain high-probability $\mathcal{O}(\log K\log\log K)$ regret for fixed and finite $T$, again with constants uniform in $δ$.

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