我们考虑在以$ s $状态的地平线$ h $和$ a $ ACTIVE的偶发性，有限的，依赖于阶段的马尔可夫决策过程的环境中进行强化学习。代理商的性能是在与环境互动以$ t $插件互动后的遗憾来衡量的。我们提出了一种乐观的后验抽样算法（OPSRL），这是一种简单的后验抽样变体，仅需要许多后样品对数，$ h $，$ s $，$ a $和$ t $ a $ h $ s $ s $ a $ a $和$ t $一对。对于OPSRL，我们保证最多可容纳订单的高概率遗憾，$ \ wideTilde {\ mathcal {o}}}（\ sqrt {h^3sat}）$忽略$ \ text {poly} \ log（hsat）$项。新型的新型技术成分是线性形式的新型抗浓缩不等式，可能具有独立感兴趣。具体而言，我们将Alfers and Dinges [1984]的Beta分布的基于正常近似的下限扩展到Dirichlet分布。我们的界限匹配订单$ \ omega（\ sqrt {h^3sat}）$的下限，从而回答了Agrawal和Jia [2017b]在情节环境中提出的空旷问题。

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth function up to a given approximation error in H\"{o}lder norms in such a way that all weights of this neural network are bounded by $1$. The latter feature is essential to control generalization errors in many statistical and machine learning applications.

加强学习（RL）的政策梯度方法非常普遍，在实践中广泛应用，但它们的性能遭受了梯度估计的较高差异。提出了几种程序来减少它，包括参与者批评（AC）和Advantag Actor-Critic（A2C）方法。最近，由于引入了深入的RL：新的控制变量（CV）和新的子采样程序都可以在复杂模型（例如神经网络）的设置中获得新的视角。基于简历的方法的重要部分是训练简历的目标功能，最受欢迎的方法是A2C的最小二乘标准。尽管取得了实际的成功，但标准并不是唯一可能的标准。在本文中，我们第一次研究称为经验方差（EV）的表现。我们在实验中观察到，不仅EV准则的性能并不比A2C差，而且有时可能会更好。除此之外，我们还证明了在非常一般的假设下实际差异的一些理论保证，并表明A2C最小二乘目标函数是EV目标的上限。我们的实验表明，就差异降低而言，基于EV的方法比A2C好得多，并且可以降低方差。

我们提出了在表格，依赖阶段的，情节的马尔可夫决策过程中使用贝叶斯-UCBVI算法进行增强学习的：Kaufmann等人的贝叶斯-UCB算法的自然扩展。 （2012年）用于多军匪徒。我们的方法将Q值函数后部的分位数用作最佳Q值函数上的上限。对于贝叶斯-UCBVI，我们证明了一个遗憾的是$ \ wideTilde {o}（\ sqrt {h^3sat}）$，其中$ h $是一集的长度，$ s $是$ s $的数量，$ a $ a $动作数量，$ t $情节数，与$ \ omega（\ sqrt {h^3sat}）$符合poly-$ \ $ \ log $ enter $ h，s，s，a，a，a，a，a ，适用于足够大的$ t $的t $。据我们所知，这是第一种获得对地平线$ h $（和$ s $）的最佳依赖性的算法，而无需涉及伯恩斯坦的奖金或噪音。对于我们的分析而言，至关重要的是一种新的细粒抗浓缩，以具有独立感兴趣的加权dirichlet总和。然后，我们解释了如何轻松地将贝叶斯-UCBVI延伸到表格环境之外，从而在我们的算法和贝叶斯引导之间表现出牢固的联系（Rubin，1981）。

我们开发了一个探索漏洞利用马尔可夫链Monte Carlo算法（$ \ OperatorName {ex ^ 2mcmc} $），它结合了多个全局提议和本地移动。所提出的方法是巨大的平行化和极其计算的高效。我们证明$ \ operatorname {ex ^ 2mcmc} $下的$ v $ v $ -unique几何ergodicity在现实条件下，并计算混合速率的显式界限，显示多个全局移动带来的改进。我们展示$ \ operatorname {ex ^ 2mcmc} $允许通过提出依赖全局移动的新方法进行微调剥削（本地移动）和探索（全球移动）。最后，我们开发了一个自适应方案，$ \ OperatorName {Flex ^ 2mcmc} $，它学习使用归一化流的全局动作的分布。我们说明了许多经典采样基准测试的$ \ OperatorName {ex ^ 2mccmc} $及其自适应版本的效率。我们还表明，这些算法提高了对基于能量的模型的抽样GAN的质量。

在这项工作中，我们对香草生成的对抗网络（GAN）的非渐近性质进行了彻底的研究。We derive theoretical guarantees for the density estimation with GANs under a proper choice of the deep neural networks classes representing generators and discriminators.特别是，我们证明了由此产生的估计会聚到真实密度$ \ mathsf {p} ^ * $以jensen-shannon（js）以$（\ log {n} / n）^ {2 \Beta /（2 \ beta + d）} $ why $ n $是样本大小和$ \ beta $ commentines $ \ mathsf {p} ^ * $的平滑度。据我们所知，这是使用Vanilla Gans的浓度估计的文献中的第一个结果，这些融合率比N ^ { - 1/2} $更快地在政权$ \ beta> D / 2 $中。此外，我们表明所获得的速率是考虑的密度类别的最低限度最佳（最高因子因子）。

Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in how relevant rules are defined. The learning procedure of PLD solves the optimization problem related to the search for rules (called probabilistic laws), which have a minimal length and relatively high probability. At inference, ensembles of these rules are used for prediction. Probabilistic laws are human-readable and PLD based models are transparent and inherently interpretable. Applications of PLD include classification/clusterization/regression tasks, as well as time series analysis/anomaly detection and adaptive (robotic) control. In this paper, we outline the main principles of PLD, highlight its benefits and limitations and provide some application guidelines.

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug-in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of cnvergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.

In many real-world scenarios, the absence of external knowledge source like Wikipedia restricts question answering systems to rely on latent internal knowledge in limited dialogue data. In addition, humans often seek answers by asking several questions for more comprehensive information. As the dialog becomes more extensive, machines are challenged to refer to previous conversation rounds to answer questions. In this work, we propose to leverage latent knowledge in existing conversation logs via a neural Retrieval-Reading system, enhanced with a TFIDF-based text summarizer refining lengthy conversational history to alleviate the long context issue. Our experiments show that our Retrieval-Reading system can exploit retrieved background knowledge to generate significantly better answers. The results also indicate that our context summarizer significantly helps both the retriever and the reader by introducing more concise and less noisy contextual information.

Transformer models have achieved superior performance in various natural language processing tasks. However, the quadratic computational cost of the attention mechanism limits its practicality for long sequences. There are existing attention variants that improve the computational efficiency, but they have limited ability to effectively compute global information. In parallel to Transformer models, state space models (SSMs) are tailored for long sequences, but they are not flexible enough to capture complicated local information. We propose SPADE, short for $\underline{\textbf{S}}$tate s$\underline{\textbf{P}}$ace $\underline{\textbf{A}}$ugmente$\underline{\textbf{D}}$ Transform$\underline{\textbf{E}}$r. Specifically, we augment a SSM into the bottom layer of SPADE, and we employ efficient local attention methods for the other layers. The SSM augments global information, which complements the lack of long-range dependency issue in local attention methods. Experimental results on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method. To further demonstrate the scalability of SPADE, we pre-train large encoder-decoder models and present fine-tuning results on natural language understanding and natural language generation tasks.