The communication complexity of secure protocols is a fundamental question of the theory of computation and has important repercussions in the development of real-life systems. As an example, the recent surge in popularity of cryptocurrencies has been enabled and accompanied by advancements in the construction of more compact cryptographic machinery. In this talk we discuss how to meet the boundaries of compactness in cryptography and how to exploit succinct communication to construct systems with new surprising properties. Specifically, we consider the problem of computing functions on encrypted data: We show how to construct a fully-homomorphic encryption scheme with message-to-ciphertext ratio (i.e. rate) of 1 – o(1), which is optimal. Along the way, we survey the implication of cryptographic compactness in different contexts, such as proof systems, scalable blockchains, and fair algorithms.

Learning is a predominant theme for any intelligent system, humans or machines. Moving beyond the classical paradigm of learning from past experience, e.g., supervised learning from given labels, a learner needs to actively collect exploratory feedback to learn the unknowns. Considerable challenges arise in such a setting, including sample complexity, costly and even outdated feedback.

In this talk, I will introduce our themed efforts on developing solutions to efficiently explore the unknowns and dynamically adjust to the changes through exploratory feedback. Specifically, I will first present our studies in leveraging special problem structures for efficient exploration. Then I will present our work on empowering the learner to detect and adjust to potential changes in the environment adaptively. Besides, I will also highlight the impact our research has generated in top-valued industry applications, including online learning to rank and interactive recommendation.