We propose a novel framework for solving continuous-time non-Markovian
stochastic control problems by means of neural rough differential equations
(Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally
arises in control problems due to the time delay effects in the system
coefficients or the driving noises, which leads to optimal control strategies
depending explicitly on the historical trajectories of the system state. By
modelling the control process as the solution of a Neural RDE driven by the
state process, we show that the control-state joint dynamics are governed by an
uncontrolled, augmented Neural RDE, allowing for fast Monte-Carlo estimation of
the value function via trajectories simulation and memory-efficient
backpropagation. We provide theoretical underpinnings for the proposed
algorithmic framework by demonstrating that Neural RDEs serve as universal
approximators for functions of random rough paths. Exhaustive numerical
experiments on non-Markovian stochastic control problems are presented, which
reveal that the proposed framework is time-resolution-invariant and achieves
higher accuracy and better stability in irregular sampling compared to existing
RNN-based approaches.

提出一种基于神经粗糙微分方程的新框架，用于解决非马尔可夫随机控制问题，通过演示控制过程作为神经粗糙微分方程的解的模型来展示控制 - 状态联合动力学如何通过一个未受控的增量神经粗糙微分方程进行管理，同时通过演示神经粗糙微分方程是随机不平滑路径函数的通用近似器来提供理论支撑，实验结果显示，这种方法比现有的基于 RNN 的方法在不规则采样下具有更高的精度和稳定性。

一种用于连续非马尔可夫随机控制问题的神经 RDE 方法

A Neural RDE approach for continuous-time non-Markovian stochastic  control problems

Diffusion Models (DMs) achieve state-of-the-art performance in generative
tasks, boosting a wave in AI for Art. Despite the success of commercialization,
DMs meanwhile provide tools for copyright violations, where infringers benefit
from illegally using paintings created by human artists to train DMs and
generate novel paintings in a similar style. In this paper, we show that it is
possible to create an image $x'$ that is similar to an image $x$ for human
vision but unrecognizable for DMs. We build a framework to define and evaluate
this adversarial example for diffusion models. Based on the framework, we
further propose AdvDM, an algorithm to generate adversarial examples for DMs.
By optimizing upon different latent variables sampled from the reverse process
of DMs, AdvDM conducts a Monte-Carlo estimation of adversarial examples for
DMs. Extensive experiments show that the estimated adversarial examples can
effectively hinder DMs from extracting their features. Our method can be a
powerful tool for human artists to protect their copyright against infringers
with DM-based AI-for-Art applications.

本文介绍了一种基于对抗样本的算法，称为 AdvDM，用于生成能够保护画家版权的扩散模型（DMs）的对抗样本。研究人员通过基于逆向过程采样的不同潜在变量实现了 Monte-Carlo 估计。大量实验表明，估计得到的对抗样本能够有效地阻止 DMs 提取其特征。

对抗样本的良性应用：通过对抗样本防止扩散模型模仿绘画

Adversarial Example Does Good: Preventing Painting Imitation from Diffusion Models via Adversarial Examples

We develop an effective generation of adversarial attacks on neural models
that output a sequence of probability distributions rather than a sequence of
single values. This setting includes the recently proposed deep probabilistic
autoregressive forecasting models that estimate the probability distribution of
a time series given its past and achieve state-of-the-art results in a diverse
set of application domains. The key technical challenge we address is
effectively differentiating through the Monte-Carlo estimation of statistics of
the joint distribution of the output sequence. Additionally, we extend prior
work on probabilistic forecasting to the Bayesian setting which allows
conditioning on future observations, instead of only on past observations. We
demonstrate that our approach can successfully generate attacks with small
input perturbations in two challenging tasks where robust decision making is
crucial: stock market trading and prediction of electricity consumption.

我们针对神经模型输出概率分布序列的情况，开发了一种更有效的对抗攻击方法。我们解决的关键技术挑战是如何通过蒙特卡罗估计输出序列的联合分布统计量。此外，我们将概率预测的先前工作扩展到贝叶斯设置中，可以对未来观测进行调节。我们证明了这种方法可以在股票市场交易和电力消耗预测等两项关键任务中成功生成具有小输入扰动的攻击。