Multi-Agent Temporal Logic Planning via Penalty Functions and Block-Coordinate Optimization

2026-02-19

AI Summary

This work addresses the challenge of high-dimensional computational complexity and scalability in multi-agent cooperative planning under Signal Temporal Logic (STL) specifications. The problem is formulated as a constrained optimization task, which is relaxed into an unconstrained form through a quadratic penalty function based on smoothed STL robustness semantics. A bilevel block coordinate gradient descent (BCGD) framework is then proposed to iteratively optimize individual agent trajectories, thereby enhancing satisfaction of the STL specification. This approach achieves scalable synthesis of multi-agent collaborative behaviors while preserving formal guarantees on specification adherence. Experimental evaluations across multiple complex multi-robot scenarios demonstrate the method’s efficiency and convergence properties.

Technology Category

• Multiagent Systems: Multiagent Planning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Multi-agent planning under Signal Temporal Logic (STL) is often hindered by collaborative tasks that lead to computational challenges due to the inherent high-dimensionality of the problem, preventing scalable synthesis with satisfaction guarantees. To address this, we formulate STL planning as an optimization program under arbitrary multi-agent constraints and introduce a penalty-based unconstrained relaxation that can be efficiently solved via a Block-Coordinate Gradient Descent (BCGD) method, where each block corresponds to a single agent's decision variables, thereby mitigating complexity. By utilizing a quadratic penalty function defined via smooth STL semantics, we show that BCGD iterations converge to a stationary point of the penalized problem under standard regularity assumptions. To enforce feasibility, the BCGD solver is embedded within a two-layer optimization scheme: inner BCGD updates are performed for a fixed penalty parameter, which is then increased in an outer loop to progressively improve multi-agent STL robustness. The proposed framework enables scalable computations and is validated through various complex multi-robot planning scenarios.

Problem

• Multi-agent planning
• Signal Temporal Logic
• Scalability
• High-dimensionality
• Collaborative tasks

Innovation

• Multi-agent planning
• Signal Temporal Logic (STL)
• Penalty function
• Block-Coordinate Gradient Descent
• Scalable optimization