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Byzantine-robust distributed learning (BRDL), in which computing devices are likely to behave abnormally due to accidental failures or malicious attacks, has recently become a hot research topic. However, even in the independent and identically distributed (i.i.d.) case, existing BRDL methods will suffer from a significant drop on model accuracy due to the large variance of stochastic gradients. Increasing batch sizes is a simple yet effective way to reduce the variance. However, when the total number of gradient computation is fixed, a too-large batch size will lead to a too-small iteration number (update number), which may also degrade the model accuracy. In view of this challenge, we mainly study the optimal batch size when the total number of gradient computation is fixed in this work. In particular, we theoretically and empirically show that when the total number of gradient computation is fixed, the optimal batch size in BRDL increases with the fraction of Byzantine workers. Therefore, compared to the case without attacks, the batch size should be set larger when under Byzantine attacks. However, for existing BRDL methods, large batch sizes will lead to a drop on model accuracy, even if there is no Byzantine attack. To deal with this problem, we propose a novel BRDL method, called Byzantine-robust stochastic gradient descent with normalized momentum (ByzSGDnm), which can alleviate the drop on model accuracy in large-batch cases. Moreover, we theoretically prove the convergence of ByzSGDnm for general non-convex cases under Byzantine attacks. Empirical results show that ByzSGDnm has a comparable performance to existing BRDL methods under bit-flipping failure, but can outperform existing BRDL methods under deliberately crafted attacks.

We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been proposed in the statistical literature. We put forward an alternative selection method based on a criterion coming from information theory and from the physics of complex systems: the bandwidth to be selected maximizes a new measure of complexity, with the aim of avoiding both overfitting and underfitting. We review existing methods of bandwidth selection and show that they lead to contradictory conclusions regarding the complexity of the probability distribution of price returns. This has also some striking consequences in the evaluation of the relevance of the efficient market hypothesis. We apply these methods to real financial data, focusing on the Bitcoin.

Zero-shot human-AI coordination holds the promise of collaborating with humans without human data. Prevailing methods try to train the ego agent with a population of partners via self-play. However, these methods suffer from two problems: 1) The diversity of a population with finite partners is limited, thereby limiting the capacity of the trained ego agent to collaborate with a novel human; 2) Current methods only provide a common best response for every partner in the population, which may result in poor zero-shot coordination performance with a novel partner or humans. To address these issues, we first propose the policy ensemble method to increase the diversity of partners in the population, and then develop a context-aware method enabling the ego agent to analyze and identify the partner's potential policy primitives so that it can take different actions accordingly. In this way, the ego agent is able to learn more universal cooperative behaviors for collaborating with diverse partners. We conduct experiments on the Overcooked environment, and evaluate the zero-shot human-AI coordination performance of our method with both behavior-cloned human proxies and real humans. The results demonstrate that our method significantly increases the diversity of partners and enables ego agents to learn more diverse behaviors than baselines, thus achieving state-of-the-art performance in all scenarios. We also open-source a human-AI coordination study framework on the Overcooked for the convenience of future studies.

Non-stationary multi-armed bandit (NS-MAB) problems have recently received significant attention. NS-MAB are typically modelled in two scenarios: abruptly changing, where reward distributions remain constant for a certain period and change at unknown time steps, and smoothly changing, where reward distributions evolve smoothly based on unknown dynamics. In this paper, we propose Discounted Thompson Sampling (DS-TS) with Gaussian priors to address both non-stationary settings. Our algorithm passively adapts to changes by incorporating a discounted factor into Thompson Sampling. DS-TS method has been experimentally validated, but analysis of the regret upper bound is currently lacking. Under mild assumptions, we show that DS-TS with Gaussian priors can achieve nearly optimal regret bound on the order of $\tilde{O}(\sqrt{TB_T})$ for abruptly changing and $\tilde{O}(T^{\beta})$ for smoothly changing, where $T$ is the number of time steps, $B_T$ is the number of breakpoints, $\beta$ is associated with the smoothly changing environment and $\tilde{O}$ hides the parameters independent of $T$ as well as logarithmic terms. Furthermore, empirical comparisons between DS-TS and other non-stationary bandit algorithms demonstrate its competitive performance. Specifically, when prior knowledge of the maximum expected reward is available, DS-TS has the potential to outperform state-of-the-art algorithms.

Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images.

Most existing studies on joint activity detection and channel estimation for grant-free massive random access (RA) systems assume perfect synchronization among all active users, which is hard to achieve in practice. Therefore, this paper considers asynchronous grant-free massive RA systems and develops novel algorithms for joint user activity detection, synchronization delay detection, and channel estimation. In particular, the framework of orthogonal approximate message passing (OAMP) is first utilized to deal with the non-independent and identically distributed (i.i.d.) pilot matrix in asynchronous grant-free massive RA systems, and an OAMP-based algorithm capable of leveraging the common sparsity among the received pilot signals from multiple base station antennas is developed. To reduce the computational complexity, a memory AMP (MAMP)based algorithm is further proposed that eliminates the matrix inversions in the OAMP-based algorithm. Simulation results demonstrate the effectiveness of the two proposed algorithms over the baseline methods. Besides, the MAMP-based algorithm reduces 37% of the computations while maintaining comparable detection/estimation accuracy, compared with the OAMP-based algorithm.

Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest. However, existing SDR methods are not suitable for analyzing datasets collected from case-control studies. In this setting, the goal is to learn and exploit the low-dimensional structure unique to or enriched by the case group, also known as the foreground group. While some unsupervised techniques such as the contrastive latent variable model and its variants have been developed for this purpose, they fail to preserve the functional relationship between the dimension-reduced covariates and the response variable. In this paper, we propose a supervised dimension reduction method called contrastive inverse regression (CIR) specifically designed for the contrastive setting. CIR introduces an optimization problem defined on the Stiefel manifold with a non-standard loss function. We prove the convergence of CIR to a local optimum using a gradient descent-based algorithm, and our numerical study empirically demonstrates the improved performance over competing methods for high-dimensional data.

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of these data sets. Thus, there has been an increased interest in efficient learning in high dimensions. Naturally, as the dimension of the input data increases, the learning task will become more difficult, due to increasing computational and statistical complexities. This makes it crucial to overcome the curse of dimensionality in a given dataset, within a reasonable time frame, in a bid to obtain the insights required to keep a competitive edge. To solve HDLSS problems, classical methods such as support vector machines can be utilised to alleviate data piling at the margin. However, when we question geometric domains and their assumptions on input data, we are naturally lead to convex optimisation problems and this gives rise to the development of solutions like distance weighted discrimination (DWD), which can be modelled as a second-order cone programming problem and solved by interior-point methods when sample size and feature dimensions of the data is moderate. In this paper, our focus is on designing an even more scalable and robust algorithm for solving large-scale generalized DWD problems.

Robots with the ability to balance time against the thoroughness of search have the potential to provide time-critical assistance in applications such as search and rescue. Current advances in ergodic coverage-based search methods have enabled robots to completely explore and search an area in a fixed amount of time. However, optimizing time against the quality of autonomous ergodic search has yet to be demonstrated. In this paper, we investigate solutions to the time-optimal ergodic search problem for fast and adaptive robotic search and exploration. We pose the problem as a minimum time problem with an ergodic inequality constraint whose upper bound regulates and balances the granularity of search against time. Solutions to the problem are presented analytically using Pontryagin's conditions of optimality and demonstrated numerically through a direct transcription optimization approach. We show the efficacy of the approach in generating time-optimal ergodic search trajectories in simulation and with drone experiments in a cluttered environment. Obstacle avoidance is shown to be readily integrated into our formulation, and we perform ablation studies that investigate parameter dependence on optimized time and trajectory sensitivity for search.

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on Qatar Riyal decomposition (RCSVD-QR). Our method utilize random sampling and the OR decomposition to address a serious bottlenck associated with classical SVD. RCSVD-QR gives satisfactory convergence speed as well as accuracy as compared to those state-of-the-art algorithms. In addition, we provides an estimate for the expected approximation error in Frobenius norm. Numerical experiments verify these claims.