The aim of the notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product of the presentation we present a succinct mathematical treatment of various topics in machine learning. The material on machine learning, along with some other related topics, is summarized in Part III, Appendix. Part I of the notes is concerned with inverse problems, employing material from Part III; Part II of the notes is concerned with data assimilation, employing material from Parts I and III.

Designing an effective communication mechanism among agents in reinforcement learning has been a challenging task, especially for real-world applications. The number of agents can grow or an environment sometimes needs to interact with a changing number of agents in real-world scenarios. To this end, a multi-agent framework needs to handle various scenarios of agents, in terms of both scales and dynamics, for being practical to real-world applications. We formulate the multi-agent environment with a different number of agents as a multi-tasking problem and propose a meta reinforcement learning (meta-RL) framework to tackle this problem. The proposed framework employs a meta-learned Communication Pattern Recognition (CPR) module to identify communication behavior and extract information that facilitates the training process. Experimental results are poised to demonstrate that the proposed framework (a) generalizes to an unseen larger number of agents and (b) allows the number of agents to change between episodes. The ablation study is also provided to reason the proposed CPR design and show such design is effective.