Cooperative Solutions to Exploration Tasks Under Speed and Budget Constraints

TL;DR

This work tackles how to coordinate multiple agents to solve dependent tasks under speed and budget constraints, allowing exploration of a solution space, inference, and budgeted queries with knowledge sharing. It introduces a formal model and algorithms for task scheduling, solution exploration, and knowledge update, evaluated on two program graphs $G_{40}$ and $G_{18}$ in a $400×400$ maze setting. Key findings show that increasing speed yields diminishing returns in highly dependent spaces, while allocating more budget to faster agents improves performance in less-dependent spaces, illustrating a clear speed-budget trade-off and the Matthew effect in resource allocation. The results offer practical guidelines for resource distribution in cooperative multi-agent systems and highlight avenues for extending the framework to dynamic rewards and real-time constraints.

Abstract

We present a multi-agent system where agents can cooperate to solve a system of dependent tasks, with agents having the capability to explore a solution space, make inferences, as well as query for information under a limited budget. Re-exploration of the solution space takes place by an agent when an older solution expires and is thus able to adapt to dynamic changes in the environment. We investigate the effects of task dependencies, with highly-dependent graph $G_{40}$ (a well-known program graph that contains $40$ highly interlinked nodes, each representing a task) and less-dependent graphs $G_{18}$ (a program graph that contains $18$ tasks with fewer links), increasing the speed of the agents and the complexity of the problem space and the query budgets available to agents. Specifically, we evaluate trade-offs between the agent's speed and query budget. During the experiments, we observed that increasing the speed of a single agent improves the system performance to a certain point only, and increasing the number of faster agents may not improve the system performance due to task dependencies. Favoring faster agents during budget allocation enhances the system performance, in line with the "Matthew effect." We also observe that allocating more budget to a faster agent gives better performance for a less-dependent system, but increasing the number of faster agents gives a better performance for a highly-dependent system.

Figures (7)

• Figure 1: Task Dependency Graph $G_{40}$
• Figure 2: Task Dependency Graph $G_{18}$
• Figure 3: Scalability testing while increasing the number of tasks for $5$ agents.
• Figure 4: Avg exploration time for individual vs cooperative agents for $G_{18}$
• Figure 5: Cooperative faster agent improves the system performance for $G_{18}$.