Finite-Bit Distributed Optimization for UAV Swarms Under Communication Bandwidth Constraints

This paper develops a unified finite-bit distributed optimization framework for UAV swarms operating over bandwidth-limited communication graphs. We consider strongly convex and smooth global objectives decomposed over local UAV cost functions and study three communication-efficient algorithmic regimes. First, we design a quantized distributed gradient-tracking descent scheme with fixed finite-bit communication and show that, under bounded quantization errors, the method converges R-linearly to a quantization-dependent neighborhood of the global optimizer. Second, we introduce an adaptive quantization strategy that dynamically adjusts the number of transmitted bits according to the current convergence stage. By forcing the quantization distortion to decay proportionally to the optimization error, the proposed adaptive scheme recovers exact linear convergence to the optimal solution while substantially reducing the cumulative communication load. Third, we develop a fully distributed 1-bit communication mode in which UAVs exchange only sign information and use coordinate-wise majority voting to aggregate both descent and consensus directions. The robust linear-contraction property is proved to a small neighborhood under a sign-Polyak–Lojasiewicz condition and a probabilistic majority-correctness assumption.