Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms

• URL: http://arxiv.org/abs/2603.20333v1
• Date: Fri, 20 Mar 2026 07:23:32 GMT
• Title: Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms
• Abstract summary: This paper studies a tri-hierarchical swarm learning system where three mechanisms act simultaneously.<n>The Bounded Total Error Theorem shows that under contractual constraints on learning rates, total suboptimality admits a component-wise upper bound uniform in time.<n>The Bounded Representation Drift Theorem gives a worst-case estimate of how Hebbian updates affect coordination-level embeddings during one MARL cycle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modern autonomous multi-agent systems combine heterogeneous learning mechanisms operating at different timescales. An open question remains: can one formally guarantee that coupled dynamics of such mechanisms stay within the admissible operational regime? This paper studies a tri-hierarchical swarm learning system where three mechanisms act simultaneously: (1) local Hebbian online learning at individual agent level (fast timescale, 10-100 ms); (2) multi-agent reinforcement learning (MARL) for tactical group coordination (medium timescale, 1-10 s); (3) meta-learning (MAML) for strategic adaptation (slow timescale, 10-100 s). Four results are established. The Bounded Total Error Theorem shows that under contractual constraints on learning rates, Lipschitz continuity of inter-level mappings, and weight stabilization, total suboptimality admits a component-wise upper bound uniform in time. The Bounded Representation Drift Theorem gives a worst-case estimate of how Hebbian updates affect coordination-level embeddings during one MARL cycle. The Meta-Level Compatibility Theorem provides sufficient conditions under which strategic adaptation preserves lower-level invariants. The Non-Accumulation Theorem proves that error does not grow unboundedly over time.

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