Compression with Distributional and Sequential Constraints

Traditional data compression methods focus on recreating data perfectly, bit-for-bit. However, the rise of Artificial Intelligence (AI) presents new challenges. In systems like robotics, distributed machine learning, and generative AI, the goal is not just accurate data transmission, but ensuring the information helps an AI agent learn, make a good decision, or generate realistic content. The success of communication should be measured by the effectiveness of the outcome, not just the accuracy of the bits.

My research develops new theories and practical algorithms for "goal-oriented" compression to address this gap. The core idea is to reframe compression as a problem with constraints on the statistical properties or the ultimate use of the data. The central technique used is an information-theoretic tool called "channel simulation," which I adapt and extend for these modern applications.

Key aims and outcomes include:
- Establishing the fundamental limits of 'universal channel simulation'-a novel problem of compression where the data's statistics are unknown-and developing practical algorithms that significantly reduce communication overhead in applications like Federated Learning.
- Constructing computationally efficient methods for high-fidelity data compression by tackling the simulation of additive Gaussian channel.
- Formalising the problem of communication-efficient distributed Reinforcement Learning, developing frameworks that drastically reduce the data transmission required to train intelligent agents over rate-constrained networks.
- Developing a formal framework for goal-oriented compression in sequential decision-making, designing policies that guide an agent to a target while minimizing communication under time and cost constraints.
- Uncovering novel theoretical connections between channel simulation and practical methods for accelerating large language models.