Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms

TL;DR

This paper analyzes a tri-hierarchical drone swarm system with multiple learning mechanisms operating at different timescales, providing formal guarantees on their coupled dynamics remaining within operational bounds.

Contribution

It introduces four theorems that establish bounds and conditions ensuring stability and invariance in multi-timescale coupled learning dynamics.

Findings

Total suboptimality is uniformly bounded over time.

Hebbian updates' impact on coordination embeddings is estimated.

Strategic adaptation preserves lower-level invariants under certain conditions.

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.