We consider optimizing a function network in the noise-free grey-box setting with RKHS function classes, where the exact intermediate results are observable. We assume that the structure of the network is known (but not the underlying functions comprising it), and we study three types of structures: (1) chain: a cascade of scalar-valued functions, (2) multi-output chain: a cascade of vector-valued functions, and (3) feed-forward network: a fully connected feed-forward network of scalar-valued functions. We propose a sequential upper confidence bound based algorithm GPN-UCB along with a general theoretical upper bound on the cumulative regret. For the Mat\'ern kernel, we additionally propose a non-adaptive sampling based method along with its theoretical upper bound on the simple regret. We also provide algorithm-independent lower bounds on the simple regret and cumulative regret, showing that GPN-UCB is near-optimal for chains and multi-output chains in broad cases of interest.

近年来，在诸如denoing，压缩感应，介入和超分辨率等反问题中使用深度学习方法的使用取得了重大进展。尽管这种作品主要是由实践算法和实验驱动的，但它也引起了各种有趣的理论问题。在本文中，我们调查了这一作品中一些突出的理论发展，尤其是生成先验，未经训练的神经网络先验和展开算法。除了总结这些主题中的现有结果外，我们还强调了一些持续的挑战和开放问题。

在本文中，我们研究了主要成分分析的问题，并采用了生成建模假设，采用了一个普通矩阵的通用模型，该模型包括涉及尖峰矩阵恢复和相位检索在内的明显特殊情况。关键假设是，基础信号位于$ l $ -Lipschitz连续生成模型的范围内，该模型具有有限的$ k $二维输入。我们提出了一个二次估计器，并证明它享有顺序的统计率$ \ sqrt {\ frac {k \ log l} {m} {m}} $，其中$ m $是样本的数量。我们还提供了近乎匹配的算法独立的下限。此外，我们提供了经典功率方法的一种变体，该方法将计算的数据投射到每次迭代期间生成模型的范围内。我们表明，在适当的条件下，该方法将指数级的快速收敛到达到上述统计率的点。我们在各种图像数据集上对峰值矩阵和相位检索模型进行实验，并说明了我们方法的性能提高到经典功率方法，并为稀疏主组件分析设计了截断的功率方法。

基于内核的模型，例如内核脊回归和高斯工艺在机器学习应用程序中无处不在，用于回归和优化。众所周知，基于内核的模型的主要缺点是高计算成本。给定$ n $样本的数据集，成本增长为$ \ Mathcal {o}（n^3）$。在某些情况下，现有的稀疏近似方法可以大大降低计算成本，从而有效地将实际成本降低到$ \ natercal {o}（n）$。尽管取得了显着的经验成功，但由于近似值而导致的误差的分析范围的现有结果仍然存在显着差距。在这项工作中，我们为NyStr \“ Om方法和稀疏变分高斯过程近似方法提供新颖的置信区间，我们使用模型的近似（代理）后差解释来建立这些方法。我们的置信区间可改善性能。回归和优化问题的界限。

在本文中，我们介绍了一个多武装的强盗问题被称为MAX-MIN分组的匪徒，其中臂在可能重叠的群体中排列，并且目标是找到最糟糕的均值奖励的组。此问题对推荐系统等应用感兴趣，并且与广泛研究的鲁棒优化问题也密切相关。我们呈现了两种基于算法的连续消除和稳健的优化，并导出了样本数量的上限，以保证找到最大最佳或近最佳组，以及算法无关的下限。我们讨论了各种兴趣案件中我们界的紧绷程度，以及衍生均匀紧张的界限。

高斯工艺（GP）是一种广泛的工具，用于依次优化黑框功能，其中评估昂贵且潜在的嘈杂。关于GP土匪的最新作品提议超越随机噪声，并设计算法对对抗性攻击的强大。本文从攻击者的角度研究了这个问题，提出了各种对抗性攻击方法，对攻击者的力量和先前信息的假设有所不同。我们的目标是从理论和实践的角度了解对GP土匪的对抗性攻击。我们主要关注对流行的GP-UCB算法的有针对性攻击和基于消除的算法的相关算法，基于对抗性扰动该函数$ f $以产生另一个函数$ \ tilde $ \ tilde {f} $，其Optima在某些目标区域中$ \ \ Mathcal {r} _ {\ rm target} $。根据我们的理论分析，我们设计了白盒攻击（已知$ F $）和黑盒攻击（未知$ F $），前者包括减法攻击和裁剪攻击，以及后者，包括激进的减法攻击。我们证明，对GP土匪的对抗性攻击也可以成功强迫该算法向$ \ Mathcal {R} _ {\ rm Target} $，即使在低攻击预算的情况下，我们也可以测试攻击对各种客观功能的有效性。

Accurate determination of a small molecule candidate (ligand) binding pose in its target protein pocket is important for computer-aided drug discovery. Typical rigid-body docking methods ignore the pocket flexibility of protein, while the more accurate pose generation using molecular dynamics is hindered by slow protein dynamics. We develop a tiered tensor transform (3T) algorithm to rapidly generate diverse protein-ligand complex conformations for both pose and affinity estimation in drug screening, requiring neither machine learning training nor lengthy dynamics computation, while maintaining both coarse-grain-like coordinated protein dynamics and atomistic-level details of the complex pocket. The 3T conformation structures we generate are closer to experimental co-crystal structures than those generated by docking software, and more importantly achieve significantly higher accuracy in active ligand classification than traditional ensemble docking using hundreds of experimental protein conformations. 3T structure transformation is decoupled from the system physics, making future usage in other computational scientific domains possible.

Adversarial imitation learning (AIL) has become a popular alternative to supervised imitation learning that reduces the distribution shift suffered by the latter. However, AIL requires effective exploration during an online reinforcement learning phase. In this work, we show that the standard, naive approach to exploration can manifest as a suboptimal local maximum if a policy learned with AIL sufficiently matches the expert distribution without fully learning the desired task. This can be particularly catastrophic for manipulation tasks, where the difference between an expert and a non-expert state-action pair is often subtle. We present Learning from Guided Play (LfGP), a framework in which we leverage expert demonstrations of multiple exploratory, auxiliary tasks in addition to a main task. The addition of these auxiliary tasks forces the agent to explore states and actions that standard AIL may learn to ignore. Additionally, this particular formulation allows for the reusability of expert data between main tasks. Our experimental results in a challenging multitask robotic manipulation domain indicate that LfGP significantly outperforms both AIL and behaviour cloning, while also being more expert sample efficient than these baselines. To explain this performance gap, we provide further analysis of a toy problem that highlights the coupling between a local maximum and poor exploration, and also visualize the differences between the learned models from AIL and LfGP.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

The Covid-19 pandemic induced a vast increase in adolescents diagnosed with eating disorders and hospitalized due to eating disorders. This immense growth stemmed partially from the stress of the pandemic but also from increased exposure to content that promotes eating disorders via social media, which, within the last decade, has become plagued by pro-eating disorder content. This study aimed to create a deep learning model capable of determining whether a given social media post promotes eating disorders based solely on image data. Tweets from hashtags that have been documented to promote eating disorders along with tweets from unrelated hashtags were collected. After prepossessing, these images were labeled as either pro-eating disorder or not based on which Twitter hashtag they were scraped from. Several deep-learning models were trained on the scraped dataset and were evaluated based on their accuracy, F1 score, precision, and recall. Ultimately, the vision transformer model was determined to be the most accurate, attaining an F1 score of 0.877 and an accuracy of 86.7% on the test set. The model, which was applied to unlabeled Twitter image data scraped from "#selfie", uncovered seasonal fluctuations in the relative abundance of pro-eating disorder content, which reached its peak in the summertime. These fluctuations correspond not only to the seasons, but also to stressors, such as the Covid-19 pandemic. Moreover, the Twitter image data indicated that the relative amount of pro-eating disorder content has been steadily rising over the last five years and is likely to continue increasing in the future.