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We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

We consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an asynchronous model where only a random portion of nodes perform computation at each iteration, while the information exchange can be conducted between all the nodes and in an asymmetric fashion. For this setting, we propose an algorithm that combines gradient tracking with a network-level variance reduction (in contrast to variance reduction within each node). This enables each node to track the average of the gradients of the objective functions. Our theoretical analysis shows that the algorithm converges linearly, when the local objective functions are strongly convex, under mild connectivity conditions on the expected mixing matrices. In particular, our result does not require the mixing matrices to be doubly stochastic. In the experiments, we investigate a broadcast mechanism that transmits information from computing nodes to their neighbors, and confirm the linear convergence of our method on both synthetic and real-world datasets.

In cell-free multiple input multiple output (MIMO) networks, multiple base stations (BSs) collaborate to achieve high spectral efficiency. Nevertheless, high penetration loss due to large blockages in harsh propagation environments is often an issue that severely degrades communication performance. Considering that intelligent reflecting surface (IRS) is capable of constructing digitally controllable reflection links in a low-cost manner, we investigate an IRS-enhanced downlink cell-free MIMO network in this paper. We aim to maximize the sum rate of all the users by jointly optimizing the transmit beamforming at the BSs and the reflection coefficients at the IRS. To address the optimization problem, we propose a fully distributed machine learning algorithm. Different from the conventional iterative optimization algorithms that require a central processing at the central processing unit (CPU) and large amount of channel state information and signaling exchange between the BSs and the CPU, in the proposed algorithm, each BS can locally design its beamforming vectors. Meanwhile, the IRS reflection coefficients are determined by one of the BSs. Simulation results show that the deployment of IRS can significantly boost the sum user rate and that the proposed algorithm can achieve a high sum user rate with a low computational complexity.

Network connectivity exposes the network infrastructure and assets to vulnerabilities that attackers can exploit. Protecting network assets against attacks requires the application of security countermeasures. Nevertheless, employing countermeasures incurs costs, such as monetary costs, along with time and energy to prepare and deploy the countermeasures. Thus, an Intrusion Response System (IRS) shall consider security and QoS costs when dynamically selecting the countermeasures to address the detected attacks. This has motivated us to formulate a joint Security-vs-QoS optimization problem to select the best countermeasures in an IRS. The problem is then transformed into a matching game-theoretical model. Considering the monetary costs and attack coverage constraints, we first derive the theoretical upper bound for the problem and later propose stable matching-based solutions to address the trade-off. The performance of the proposed solution, considering different settings, is validated over a series of simulations.

This paper studies the covariance based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system, where the active devices transmit their signature sequences to multiple base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. The scaling law of covariance based activity detection in the single-cell scenario has been thoroughly analyzed in the literature. This paper aims to analyze the scaling law of covariance based activity detection in the multi-cell massive MIMO system. In particular, this paper shows a quadratic scaling law in the multi-cell system under the assumption that the exponent in the classical path-loss model is greater than 2, which demonstrates that in the multi-cell MIMO system the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells (as the number of antennas tends to infinity). This paper also characterizes the distribution of the estimation error in the multi-cell scenario.

Deep reinforcement learning algorithms can perform poorly in real-world tasks due to the discrepancy between source and target environments. This discrepancy is commonly viewed as the disturbance in transition dynamics. Many existing algorithms learn robust policies by modeling the disturbance and applying it to source environments during training, which usually requires prior knowledge about the disturbance and control of simulators. However, these algorithms can fail in scenarios where the disturbance from target environments is unknown or is intractable to model in simulators. To tackle this problem, we propose a novel model-free actor-critic algorithm -- namely, state-conservative policy optimization (SCPO) -- to learn robust policies without modeling the disturbance in advance. Specifically, SCPO reduces the disturbance in transition dynamics to that in state space and then approximates it by a simple gradient-based regularizer. The appealing features of SCPO include that it is simple to implement and does not require additional knowledge about the disturbance or specially designed simulators. Experiments in several robot control tasks demonstrate that SCPO learns robust policies against the disturbance in transition dynamics.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Properly handling missing data is a fundamental challenge in recommendation. Most present works perform negative sampling from unobserved data to supply the training of recommender models with negative signals. Nevertheless, existing negative sampling strategies, either static or adaptive ones, are insufficient to yield high-quality negative samples --- both informative to model training and reflective of user real needs. In this work, we hypothesize that item knowledge graph (KG), which provides rich relations among items and KG entities, could be useful to infer informative and factual negative samples. Towards this end, we develop a new negative sampling model, Knowledge Graph Policy Network (KGPolicy), which works as a reinforcement learning agent to explore high-quality negatives. Specifically, by conducting our designed exploration operations, it navigates from the target positive interaction, adaptively receives knowledge-aware negative signals, and ultimately yields a potential negative item to train the recommender. We tested on a matrix factorization (MF) model equipped with KGPolicy, and it achieves significant improvements over both state-of-the-art sampling methods like DNS and IRGAN, and KG-enhanced recommender models like KGAT. Further analyses from different angles provide insights of knowledge-aware sampling. We release the codes and datasets at //github.com/xiangwang1223/kgpolicy.

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.