Graph Spanners
Given a graph G, a graph spanner is, informally, a subgraph that preserves lengths of shortest paths in G up to some amount of distortion (typically multiplicative and/or additive). Computing sparse or low weight graph spanners has theoretical and practical applications in various network design problems, including those in distributed computing and communication networks. Additionally, many graph spanner problems can be seen as generalizations of other well-known problems (e.g., the minimum spanning tree or minimum Steiner tree problems are special cases where the distortion is allowed to be arbitrarily large). This document provides a survey on the current literature of graph spanners, including different problem variants, hardness results, common techniques, and related open problems. The focus is on a method-based tutorial style which will allow those unfamiliar with the area to survey the problems considered and typical techniques used in the literature to compute spanners.
Graph Spanners: A Tutorial Review …

Renewal Monte Carlo (RMC)
In this paper, we present an online reinforcement learning algorithm, called Renewal Monte Carlo (RMC), for infinite horizon Markov decision processes with a designated start state. RMC is a Monte Carlo algorithm and retains the advantages of Monte Carlo methods including low bias, simplicity, and ease of implementation while, at the same time, circumvents their key drawbacks of high variance and delayed (end of episode) updates. The key ideas behind RMC are as follows. First, under any reasonable policy, the reward process is ergodic. So, by renewal theory, the performance of a policy is equal to the ratio of expected discounted reward to the expected discounted time over a regenerative cycle. Second, by carefully examining the expression for performance gradient, we propose a stochastic approximation algorithm that only requires estimates of the expected discounted reward and discounted time over a regenerative cycle and their gradients. We propose two unbiased estimators for evaluating performance gradients—a likelihood ratio based estimator and a simultaneous perturbation based estimator—and show that for both estimators, RMC converges to a locally optimal policy. We generalize the RMC algorithm to post-decision state models and also present a variant that converges faster to an approximately optimal policy. We conclude by presenting numerical experiments on a randomly generated MDP, event-triggered communication, and inventory management. …

RObust regression algorithm via Online Feature Selection (RoOFS)
The presence of data corruption in user-generated streaming data, such as social media, motivates a new fundamental problem that learns reliable regression coefficient when features are not accessible entirely at one time. Until now, several important challenges still cannot be handled concurrently: 1) corrupted data estimation when only partial features are accessible; 2) online feature selection when data contains adversarial corruption; and 3) scaling to a massive dataset. This paper proposes a novel RObust regression algorithm via Online Feature Selection (\textit{RoOFS}) that concurrently addresses all the above challenges. Specifically, the algorithm iteratively updates the regression coefficients and the uncorrupted set via a robust online feature substitution method. We also prove that our algorithm has a restricted error bound compared to the optimal solution. Extensive empirical experiments in both synthetic and real-world datasets demonstrated that the effectiveness of our new method is superior to that of existing methods in the recovery of both feature selection and regression coefficients, with very competitive efficiency. …

Bilingual-GAN
Latent space based GAN methods and attention based sequence to sequence models have achieved impressive results in text generation and unsupervised machine translation respectively. Leveraging the two domains, we propose an adversarial latent space based model capable of generating parallel sentences in two languages concurrently and translating bidirectionally. The bilingual generation goal is achieved by sampling from the latent space that is shared between both languages. First two denoising autoencoders are trained, with shared encoders and back-translation to enforce a shared latent state between the two languages. The decoder is shared for the two translation directions. Next, a GAN is trained to generate synthetic ‘code’ mimicking the languages’ shared latent space. This code is then fed into the decoder to generate text in either language. We perform our experiments on Europarl and Multi30k datasets, on the English-French language pair, and document our performance using both supervised and unsupervised machine translation. …