预处理一直是优化和机器学习方面的主食技术。它通常会减少其应用于矩阵的条件数，从而加快优化算法的收敛性。尽管实践中有许多流行的预处理技术，但大多数人缺乏降低病数的理论保证。在本文中，我们研究了最佳对角线预处理的问题，以分别或同时分别或同时缩放其行或列来实现任何全级矩阵的条件数量的最大降低。我们首先将问题重新将问题重新制定为一个准凸出问题，并提供了一种基线一分配算法，该算法在实践中易于实现，其中每次迭代都包含SDP可行性问题。然后，我们建议使用$ o（\ log（\ frac {1} {\ epsilon}）））$迭代复杂度提出多项式时间潜在的降低算法，其中每个迭代均由基于Nesterov-todd方向的牛顿更新组成。我们的算法基于该问题的表述，该问题是von Neumann最佳生长问题的广义版本。接下来，我们专注于单方面的最佳对角线预处理问题，并证明它们可以作为标准双SDP问题配方，我们应用了有效的定制求解器并研究我们最佳的对角线预处理的经验性能。我们在大型矩阵上进行的广泛实验表明，与基于启发式的预处理相比，最佳对角线预处理在减少条件数方面的实际吸引力。

我们引入了一种降低尺寸的二阶方法（DRSOM），用于凸和非凸的不受约束优化。在类似信任区域的框架下，我们的方法保留了二阶方法的收敛性，同时仅在两个方向上使用Hessian-Vector产品。此外，计算开销仍然与一阶相当，例如梯度下降方法。我们证明该方法的复杂性为$ O（\ epsilon^{ - 3/2}）$，以满足子空间中的一阶和二阶条件。DRSOM的适用性和性能通过逻辑回归，$ L_2-L_P $最小化，传感器网络定位和神经网络培训的各种计算实验展示。对于神经网络，我们的初步实施似乎在训练准确性和迭代复杂性方面与包括SGD和ADAM在内的最先进的一阶方法获得了计算优势。

回归学习是经典的，是医学图像分析的基础。它为许多关键应用程序提供了连续的映射，例如属性估计，对象检测，分割和非刚性注册。但是，先前的研究主要以案例标准（如均方误差）为优化目标。他们忽略了非常重要的人口相关标准，这正是许多任务中的最终评估指标。在这项工作中，我们建议通过有关直接优化细粒相关损失的新型研究来重新审视经典回归任务。我们主要探索两个互补相关索引作为可学习的损失：Pearson线性相关（PLC）和Spearman等级相关性（SRC）。本文的贡献是两个折叠。首先，对于全球层面的PLC，我们提出了一项策略，以使其对异常值进行强大的态度并规范关键分布因素。这些努力显着稳定学习并扩大了PLC的功效。其次，对于本地级别的SRC，我们提出了一种粗到精细的方案，以减轻样品之间确切排名顺序的学习。具体而言，我们将样本排名的学习转换为样本之间相似关系的学习。我们在两个典型的超声图像回归任务上广泛验证了我们的方法，包括图像质量评估和生物措施测量。实验证明，通过直接优化相关性的细粒度指导，回归性能得到显着提高。我们提出的相关性损失是一般的，可以扩展到更重要的应用程序。

在Fisher市场中，代理商（用户）花费（人造）货币预算来购买最大化其公用事业的商品，而中央规划师则将其设定为容量约束的商品，以便市场清算。但是，定价方案在Fisher市场实现平衡结果方面的功效通常取决于用户的预算和公用事业的完全了解，并且要求交易在同时存在所有用户的静态市场中发生。结果，我们研究了Fisher市场的在线变体，其中有私人公用事业和预算参数的预算受限用户，绘制了I.I.D.从分配$ \ Mathcal {d} $，顺序输入市场。在这种情况下，我们开发了一种仅根据用户消费的观察结果来调整价格的算法用户数量和良好的能力量表为$ O（n）$。在这里，我们的遗憾措施是在线算法和离线甲骨文之间的艾森伯格 - 盖尔计划目标的最佳差距，并提供有关用户预算和公用事业的完整信息。为了确定我们方法的功效，我们证明了任何统一（静态）定价算法，包括设定预期平衡价格并完全了解分销$ \ MATHCAL {D} $的算法，既无法实现遗憾和限制的违反比$ \ omega（\ sqrt {n}）$。虽然我们揭示的偏好算法不需要对分布$ \ MATHCAL {d} $不了解，但我们表明，如果$ \ Mathcal {d} $是已知的，则是预期的平衡定价Achieves $ O（\ log（\ log（n））的自适应变体）$遗憾和离散分发的恒定容量违反。最后，我们提出了数值实验，以证明相对于几个基准测试的揭示偏好算法的性能。

我们提出了一个数据驱动的投资组合选择模型，该模型使用分布稳健优化的框架来整合侧面信息，条件估计和鲁棒性。投资组合经理在观察到的侧面信息上进行条件解决了一个分配问题，该问题可最大程度地减少最坏情况下的风险回收权衡权衡，但要受到最佳运输歧义集中协变量返回概率分布的所有可能扰动。尽管目标函数在概率措施中的非线性性质非线性，但我们表明，具有侧面信息问题的分布稳健的投资组合分配可以作为有限维优化问题进行重新纠正。如果基于均值变化或均值的风险标准做出投资组合的决策，则可以进一步简化所得的重新制定为二阶或半明确锥体程序。美国股票市场的实证研究证明了我们对其他基准的综合框架的优势。

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.

For Prognostics and Health Management (PHM) of Lithium-ion (Li-ion) batteries, many models have been established to characterize their degradation process. The existing empirical or physical models can reveal important information regarding the degradation dynamics. However, there is no general and flexible methods to fuse the information represented by those models. Physics-Informed Neural Network (PINN) is an efficient tool to fuse empirical or physical dynamic models with data-driven models. To take full advantage of various information sources, we propose a model fusion scheme based on PINN. It is implemented by developing a semi-empirical semi-physical Partial Differential Equation (PDE) to model the degradation dynamics of Li-ion-batteries. When there is little prior knowledge about the dynamics, we leverage the data-driven Deep Hidden Physics Model (DeepHPM) to discover the underlying governing dynamic models. The uncovered dynamics information is then fused with that mined by the surrogate neural network in the PINN framework. Moreover, an uncertainty-based adaptive weighting method is employed to balance the multiple learning tasks when training the PINN. The proposed methods are verified on a public dataset of Li-ion Phosphate (LFP)/graphite batteries.

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is of high possibility to be degraded due to noises and distortions. In this paper, we propose two novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (i.e., signal and object)-domain curvature regularization model. Fast numerical optimization algorithms are developed relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, which are further accelerated by GPU implementation. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS.

Masked image modeling (MIM) has shown great promise for self-supervised learning (SSL) yet been criticized for learning inefficiency. We believe the insufficient utilization of training signals should be responsible. To alleviate this issue, we introduce a conceptually simple yet learning-efficient MIM training scheme, termed Disjoint Masking with Joint Distillation (DMJD). For disjoint masking (DM), we sequentially sample multiple masked views per image in a mini-batch with the disjoint regulation to raise the usage of tokens for reconstruction in each image while keeping the masking rate of each view. For joint distillation (JD), we adopt a dual branch architecture to respectively predict invisible (masked) and visible (unmasked) tokens with superior learning targets. Rooting in orthogonal perspectives for training efficiency improvement, DM and JD cooperatively accelerate the training convergence yet not sacrificing the model generalization ability. Concretely, DM can train ViT with half of the effective training epochs (3.7 times less time-consuming) to report competitive performance. With JD, our DMJD clearly improves the linear probing classification accuracy over ConvMAE by 5.8%. On fine-grained downstream tasks like semantic segmentation, object detection, etc., our DMJD also presents superior generalization compared with state-of-the-art SSL methods. The code and model will be made public at https://github.com/mx-mark/DMJD.

Reinforcement learning (RL) is one of the most important branches of AI. Due to its capacity for self-adaption and decision-making in dynamic environments, reinforcement learning has been widely applied in multiple areas, such as healthcare, data markets, autonomous driving, and robotics. However, some of these applications and systems have been shown to be vulnerable to security or privacy attacks, resulting in unreliable or unstable services. A large number of studies have focused on these security and privacy problems in reinforcement learning. However, few surveys have provided a systematic review and comparison of existing problems and state-of-the-art solutions to keep up with the pace of emerging threats. Accordingly, we herein present such a comprehensive review to explain and summarize the challenges associated with security and privacy in reinforcement learning from a new perspective, namely that of the Markov Decision Process (MDP). In this survey, we first introduce the key concepts related to this area. Next, we cover the security and privacy issues linked to the state, action, environment, and reward function of the MDP process, respectively. We further highlight the special characteristics of security and privacy methodologies related to reinforcement learning. Finally, we discuss the possible future research directions within this area.