  Scalable and efficient distributed learning is one of the main driving forces
behind the recent rapid advancement of machine learning and artificial
intelligence. One prominent feature of this topic is that recent progresses
have been made by researchers in two communities: (1) the system community such
as database, data management, and distributed systems, and (2) the machine
learning and mathematical optimization community. The interaction and knowledge
sharing between these two communities has led to the rapid development of new
distributed learning systems and theory.
  In this work, we hope to provide a brief introduction of some distributed
learning techniques that have recently been developed, namely lossy
communication compression (e.g., quantization and sparsification), asynchronous
communication, and decentralized communication. One special focus in this work
is on making sure that it can be easily understood by researchers in both
communities -- On the system side, we rely on a simplified system model hiding
many system details that are not necessary for the intuition behind the system
speedups; while, on the theory side, we rely on minimal assumptions and
significantly simplify the proof of some recent work to achieve comparable
results.
