---
title: "Neural Actor--Critic Learning with Minimax Critics and Reflected Langevin Sampling"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.03352v1"
permalink: "https://feed.astralor.com/items/itm_eb682f6c7f2fcf9c4bb86455"
published: "2026-11-02T16:05:40.000Z"
score: 56
channel: "finance"
tags: ["LLM","多模态","Neural Actor--Critic Learning","Minimax Critics","Reflected Langevin Sampling","Actor--critic","Bellman","Langevin"]
---

# Neural Actor--Critic Learning with Minimax Critics and Reflected Langevin Sampling

## At a glance

Actor--critic methods rely on critic gradients to improve continuous-action policies, yet finite-sample guarantees must control both value and gradient errors and their propagation through the actor. We develop a neural…

## Key points

- Actor--critic methods rely on critic gradients to improve continuous-action policies, yet finite-sample guarantees must control both value and gradient errors and their propagation through the actor.
- We develop a neural actor-critic procedure that combines a regularized minimax Bellman estimator over sigmoid networks with a finite reflected Langevin sampler driven by the fitted critic gradient.
- Under uniform Bellman regularity and covered reset sampling, a positive high-order action-derivative penalty yields value and action-gradient risk bounds with classical nonparametric minimax exponents up to logarithmic …

## Full text

Actor--critic methods rely on critic gradients to improve continuous-action policies, yet finite-sample guarantees must control both value and gradient errors and their propagation through the actor. We develop a neural actor-critic procedure that combines a regularized minimax Bellman estimator over sigmoid networks with a finite reflected Langevin sampler driven by the fitted critic gradient. Under uniform Bellman regularity and covered reset sampling, a positive high-order action-derivative penalty yields value and action-gradient risk bounds with classical nonparametric minimax exponents up to logarithmic factors. We propagate estimation, mixing, discretization, temperature, and policy-iteration errors to obtain return guarantees, with refinements for bounded multimodal potentials and strongly concave regimes. Empirical studies across controlled simulations, logged continuous-control data, and a simulated decision task show favorable performance relative to the considered baselines.

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