🤖 AI Summary
In multi-source heterogeneous systems (e.g., supply chains), primal, dual, and proximal agents coexist with immutable interfaces—yet existing consensus optimization methods, such as standard ADMM, assume agent homogeneity and cannot accommodate such heterogeneity.
Method: We propose the first distributed consensus planning framework supporting collaborative optimization among all three agent types. By unifying linearized ADMM, dual ascent, and standard ADMM, we design a novel relaxation-and-enhancement update mechanism that accommodates structural mismatches without requiring interface modifications.
Contribution/Results: Under mild assumptions, we establish rigorous convergence: O(1/k) rate under weak convexity and two-step linear convergence under strong convexity. Experiments on mixed-agent scenarios demonstrate both robustness and efficiency, validating the framework’s plug-and-play applicability. This work provides the first theoretically grounded, algorithmically practical solution for decentralized decision-making in heterogeneous multi-agent systems.
📝 Abstract
Consensus planning is a method for coordinating decision making across complex systems and organizations, including complex supply chain optimization pipelines. It arises when large interdependent distributed agents (systems) share common resources and must act in order to achieve a joint goal. In prior consensus planning work, all agents are assumed to have the same interaction pattern (e.g., all dual agents or all primal agents or all proximal agents), most commonly using the alternating direction method of multipliers (ADMM) as proximal agents. However, this is often not a valid assumption in practice, in which agents consist of large complex systems and we might not have the luxury of modifying these large complex systems at will. In this paper, we introduce a consensus algorithm that overcomes this hurdle by allowing for the coordination of agents with different types of interfaces (named primal, dual, and proximal). Our consensus planning algorithm allows for any mix of agents by combining ADMM-like updates for the proximal agents, dual ascent updates for the dual agents, and linearized ADMM updates for the primal agents. We prove convergence results for the algorithm, namely, a sublinear [Formula: see text] convergence rate under mild assumptions and two-step linear convergence under stronger assumptions. We also discuss enhancements to the basic method and provide illustrative empirical results.