TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: This paper considers multi-agent reinforcement learning (MARL) in networked system control. Specifically, each agent learns a decentralized control policy based on local observations and messages from connected neighbors. We formulate such a networked MARL (NMARL) problem as a spatiotemporal Markov decision process and introduce a spatial discount factor to stabilize the training of each local agent. Further, we propose a new differentiable communication protocol, called NeurComm, to reduce information loss and non-stationarity in NMARL. Based on experiments in realistic NMARL scenarios of adaptive traffic signal control and cooperative adaptive cruise control, an appropriate spatial discount factor effectively enhances the learning curves of non-communicative MARL algorithms, while NeurComm outperforms existing communication protocols in both learning efficiency and control performance.

SOLUTION: This paper proposes a new formulation and a new communication protocol for networked multi-agent control problems

PROBLEM: Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging  this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem and establish $O(\epsilon^{-4})$ complexity for finding $\epsilon$-first-order stationary point, in which the algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by~\citep{iusem2017extragradient}. Then we propose an adaptive variant of OSG named Optimistic Adagrad (OAdagrad) and reveal an \emph{improved} adaptive complexity $\widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $\widetilde{O}(\cdot)$ compresses a logarithmic factor of $\epsilon$. }, where $\alpha$ characterizes the growth rate of the cumulative stochastic gradient and $0\leq \alpha\leq 1/2$. To the best of our knowledge, this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization. Empirically, our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training. Moreover, this observation can be explained by the slow growth rate of the cumulative stochastic gradient, as observed empirically.

SOLUTION: This paper provides novel analysis of adaptive gradient algorithms for solving non-convex non-concave min-max problems as GANs, and explains the reason why adaptive gradient methods outperform its non-adaptive counterparts by empirical studies.

PROBLEM: Self-normalizing discriminative models approximate the normalized probability of a class without having to compute the partition function. This property is useful to computationally-intensive neural network classifiers, as the cost of computing the partition function grows linearly with the number of classes and may become prohibitive. In particular, since neural language models may deal with up to millions of classes, their self-normalization properties received notable attention. Several
 recent studies empirically found that language models, trained using Noise Contrastive Estimation (NCE), exhibit self-normalization, but could not explain why. In this study, we provide a theoretical justification to this property by viewing
 NCE as a low-rank matrix approximation. Our empirical investigation compares NCE to the alternative explicit approach for self-normalizing language models. It also uncovers a surprising negative correlation between self-normalization and
 perplexity, as well as some regularity in the observed errors that may potentially be used for improving self-normalization algorithms in the future.

SOLUTION:
We prove that NCE is self-normalized and demonstrate it on datasets