To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine learning, communications, and many other fields. Despite its broad applications in nonconvex optimization, for a great number of nonconvex and nonsmooth objective functions, its theoretical convergence guarantee is still an open problem. In this paper, we propose a two-block linearized ADMM and a multi-block parallel linearized ADMM for problems with nonconvex and nonsmooth objectives. Mathematically, we present that the algorithms can converge for a broader class of objective functions under less strict assumptions compared with previous works. Furthermore, our proposed algorithm can update coupled variables in parallel and work for less restrictive nonconvex problems, where the traditional ADMM may have difficulties in solving subproblems.

Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP), based on a single trajectory of Markovian samples induced by a behavior policy. Focusing on a $\gamma $ -discounted MDP with state space $\mathcal {S}$ and action space $\mathcal {A}$ , we demonstrate that the $\ell _{\infty }$ -based sample complexity of classical asynchronous Q-learning — namely, the number of samples needed to yield an entrywise $\varepsilon $ -accurate estimate of the Q-function — is at most on the order of $\frac {1}{ \mu _{\mathsf {min}}(1-\gamma)^{5}\varepsilon ^{2}}+ \frac { t_{\mathsf {mix}}}{ \mu _{\mathsf {min}}(1-\gamma)}$ up to some logarithmic factor, provided that a proper constant learning rate is adopted. Here, $t_{\mathsf {mix}}$ and $\mu _{\mathsf {min}}$ denote respectively the mixing time and the minimum state-action occupancy probability of the sample trajectory. The first term of this bound matches the sample complexity in the synchronous case with independent samples drawn from the stationary distribution of the trajectory. The second term reflects the cost taken for the empirical distribution of the Markovian trajectory to reach a steady state, which is incurred at the very beginning and becomes amortized as the algorithm runs. Encouragingly, the above bound improves upon the state-of-the-art result by a factor of at least $|\mathcal {S}||\mathcal {A}|$ for all scenarios, and by a factor of at least $t_{\mathsf {mix}}|\mathcal {S}||\mathcal {A}|$ for any sufficiently small accuracy level $\varepsilon $ . Further, we demonstrate that the scaling on the effective horizon $\frac {1}{1-\gamma }$ can be improved by means of variance reduction.

In the burgeoning ecosystem of Internet of Things, multivariate time series (MTS) data has become ubiquitous, highlighting the fundamental role of time series forecasting across numerous applications. The crucial challenge of long-term MTS forecasting requires adept models capable of capturing both intra-and inter-series dependencies. Recent advancements in deep learning, notably Transformers, have shown promise. However, many prevailing methods either marginalize inter-series dependencies or overlook them entirely. To bridge this gap, this paper introduces a novel series-aware framework, explicitly designed to emphasize the significance of such dependencies. At the heart of this framework lies our specific implementation: the SageFormer. As a Series-aware Graph-enhanced Transformer model, SageFormer proficiently discerns and models the intricate relationships between series using graph structures. Beyond capturing diverse temporal patterns, it also curtails redundant information across series. Notably, the series-aware framework seamlessly integrates with existing Transformer-based models, enriching their ability to comprehend inter-series relationships. Extensive experiments on real-world and synthetic datasets validate the superior performance of SageFormer against contemporary state-of-the-art approaches.

This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. One class of algorithms use communications between some or all pairs of adjacent agents at each iteration. Another class of algorithms uses a random walk incremental strategy, which sequentially activates a succession of agents. Existing incremental algorithms require diminishing step sizes to converge to the solution, and their convergence is slow. In this work, we propose a random walk algorithm that uses a fixed step size and converges faster to the solution than the existing random walk incremental algorithms. Our algorithm uses only one link to communicate the latest information for an agent to another. Since this style of communication mimics a man walking in a network, we call our algorithm Walkman. We establish convergence for convex and nonconvex objectives. For decentralized least squares, we derive a linear rate of convergence and obtain a better communication complexity than those of other decentralized algorithms. Numerical experiments verify our analysis results.

Conventional direction-of-arrival (DOA) estimators are vulnerable to impulsive noise. In this work, to tackle this issue, a class of weakly convex-inducing penalties is introduced for robust DOA estimation via low-rank matrix approximation, where $\ell_{2,1}$ -norm is adopted as the metric for suppressing the outliers. Two iterative algorithms are developed to construct the noise-free data matrix. To avoid determining the number of sources, the DOAs are estimated by exploiting the special joint diagonalization structure of the constructed signal covariance matrix. Compared with several existing algorithms, the proposed methods enjoy faster computation, similar DOA estimation performance against impulsive noise and requiring no a priori information of the source number. Numerical experiments are included to demonstrate the outlier-resistance of our solutions.