How to optimize non-smooth functions with linear constraints using block-coordinate methods?
PARAMETRIZATION AND CONVERGENCE OF A PRIMAL-DUAL BLOCK-COORDINATE APPROACH TO LINEARLY-CONSTRAINED NONSMOOTH OPΤΙΜΙΖΑΤION
August 30, 2024
https://arxiv.org/pdf/2408.16424This paper proposes a decentralized algorithm for solving optimization problems where multiple agents control distinct blocks of variables, relevant to scenarios like optimal resource allocation or distributed control in multi-agent systems. While not directly about LLMs, the key points relevant to LLM-based systems are:
- Decentralized computation: Each agent updates its variables independently using local information and communication with a central coordinator, suitable for situations where agents have limited communication bandwidth or privacy concerns.
- Handling large-scale problems: The algorithm uses random block coordinate updates, making it suitable for problems with a large number of variables, as often encountered in LLM applications.
- Convergence guarantees: The paper provides theoretical guarantees for the algorithm's convergence under specific conditions, important for ensuring the reliability of multi-agent systems.
This approach could be relevant for developing collaborative LLM applications where multiple agents, each with their own LLM, work together to solve complex tasks.