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We study stochastic Cubic Newton methods for solving general possibly non-convex minimization problems. We propose a new framework, which we call the helper framework, that provides a unified view of the stochastic and variance-reduced second-order algorithms equipped with global complexity guarantees. It can also be applied to learning with auxiliary information. Our helper framework offers the algorithm designer high flexibility for constructing and analyzing the stochastic Cubic Newton methods, allowing arbitrary size batches, and the use of noisy and possibly biased estimates of the gradients and Hessians, incorporating both the variance reduction and the lazy Hessian updates. We recover the best-known complexities for the stochastic and variance-reduced Cubic Newton, under weak assumptions on the noise. A direct consequence of our theory is the new lazy stochastic second-order method, which significantly improves the arithmetic complexity for large dimension problems. We also establish complexity bounds for the classes of gradient-dominated objectives, that include convex and strongly convex problems. For Auxiliary Learning, we show that using a helper (auxiliary function) can outperform training alone if a given similarity measure is small.

In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference solution. When fast convergence in few iterations can be accomplished the algorithm is able to generate wall-time reduction in comparison to the serial computation. We chose the laminar flow around a cylinder benchmark on 2-dimensional domain which was simulated with the open-source software OpenFoam. The numerical experiments presented in this work aim to approximate states local in time and space and the diagnostic lift coefficient. The Reynolds number is gradually increased from 100 to 1,000, before the transition to turbulent flows sets in. After the results are presented the convergence behavior is discussed with respect to the Reynolds number and the applied interpolation schemes.

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples.

This paper discusses the geometrical features and wideband performance of the beam with maximal ratio combining coefficients for a generic multi-antenna receiver. In particular, in case the channel is a linear combination of plane waves, we show that such a beam can be decomposed in a linear combination of beams pointed in the direction of each plane wave, and we compute how many directions can be effectively utilized. This highlights that such beam is better exploiting the spatial diversity provided by the channel, and therefore it is expected to be more robust to disruptions. Moreover, we compute the achieved Signal-to-Noise-Ratio for a wideband receiver, showing that it is not significantly worse than for other methods. Finally, we provide some insights on the robustness of the method by simulating the impact of the blockage of one multipath components.

This paper proposes an extension of Random Projection Depth (RPD) to cope with multiple modalities and non-convexity on data clouds. In the framework of the proposed method, the RPD is computed in a reproducing kernel Hilbert space. With the help of kernel principal component analysis, we expect that the proposed method can cope with the above multiple modalities and non-convexity. The experimental results demonstrate that the proposed method outperforms RPD and is comparable to other existing detection models on benchmark datasets regarding Area Under the Curves (AUCs) of Receiver Operating Characteristic (ROC).

The protection of Industrial Control Systems (ICS) that are employed in public critical infrastructures is of utmost importance due to catastrophic physical damages cyberattacks may cause. The research community requires testbeds for validation and comparing various intrusion detection algorithms to protect ICS. However, there exist high barriers to entry for research and education in the ICS cybersecurity domain due to expensive hardware, software, and inherent dangers of manipulating real-world systems. To close the gap, built upon recently developed 3D high-fidelity simulators, we further showcase our integrated framework to automatically launch cyberattacks, collect data, train machine learning models, and evaluate for practical chemical and manufacturing processes. On our testbed, we validate our proposed intrusion detection model called Minimal Threshold and Window SVM (MinTWin SVM) that utilizes unsupervised machine learning via a one-class SVM in combination with a sliding window and classification threshold. Results show that MinTWin SVM minimizes false positives and is responsive to physical process anomalies. Furthermore, we incorporate our framework with ICS cybersecurity education by using our dataset in an undergraduate machine learning course where students gain hands-on experience in practicing machine learning theory with a practical ICS dataset. All of our implementations have been open-sourced.

Offline Reinforcement Learning (RL) methods leverage previous experiences to learn better policies than the behavior policy used for data collection. In contrast to behavior cloning, which assumes the data is collected from expert demonstrations, offline RL can work with non-expert data and multimodal behavior policies. However, offline RL algorithms face challenges in handling distribution shifts and effectively representing policies due to the lack of online interaction during training. Prior work on offline RL uses conditional diffusion models to represent multimodal behavior in the dataset. Nevertheless, these methods are not tailored toward alleviating the out-of-distribution state generalization. We introduce a novel method named State Reconstruction for Diffusion Policies (SRDP), incorporating state reconstruction feature learning in the recent class of diffusion policies to address the out-of-distribution generalization problem. State reconstruction loss promotes generalizable representation learning of states to alleviate the distribution shift incurred by the out-of-distribution (OOD) states. We design a novel 2D Multimodal Contextual Bandit environment to illustrate the OOD generalization and faster convergence of SRDP compared to prior algorithms. In addition, we assess the performance of our model on D4RL continuous control benchmarks, namely the navigation of an 8-DoF ant and forward locomotion of half-cheetah, hopper, and walker2d, achieving state-of-the-art results.

With the rapid progress in Multi-Agent Path Finding (MAPF), researchers have studied how MAPF algorithms can be deployed to coordinate hundreds of robots in large automated warehouses. While most works try to improve the throughput of such warehouses by developing better MAPF algorithms, we focus on improving the throughput by optimizing the warehouse layout. We show that, even with state-of-the-art MAPF algorithms, commonly used human-designed layouts can lead to congestion for warehouses with large numbers of robots and thus have limited scalability. We extend existing automatic scenario generation methods to optimize warehouse layouts. Results show that our optimized warehouse layouts (1) reduce traffic congestion and thus improve throughput, (2) improve the scalability of the automated warehouses by doubling the number of robots in some cases, and (3) are capable of generating layouts with user-specified diversity measures. We include the source code at: //github.com/lunjohnzhang/warehouse_env_gen_public

Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.