Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915878068551680 |
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| author | Bychkov, Oleksii |
| author_facet | Bychkov, Oleksii |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20333 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms Bychkov, Oleksii Machine Learning Artificial Intelligence Multiagent Systems 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. |
| title | Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms |
| topic | Machine Learning Artificial Intelligence Multiagent Systems |
| url | https://arxiv.org/abs/2603.20333 |