PBA-TEQ algorithm slashes multi-agent communication to logarithmic bit rates

A team led by Zihao Ren from the Systems and Control group has published a paper on arXiv introducing quantization techniques that dramatically reduce communication costs in distributed Nash equilibrium (NE) seeking. In multi-agent network games, agents iteratively exchange messages to converge to equilibrium, but the digital channel bandwidth often becomes a bottleneck. The authors propose a general class of ultimate-boundedness-based quantizers, combining sparsification and uniform quantization, to compress messages without sacrificing convergence.

Their core contribution is PBA-TEQ (Passivity-Based NE seeking Algorithm with Time-varying scaling Error state Quantization), which achieves linear convergence under a sufficient condition. More strikingly, when paired with either a scalarization or greedy quantizer, the algorithm guarantees unbiased linear convergence with a communication complexity of just log₂(O(nd)) bits per transmission, where n is the number of agents and d is the decision-state dimension. That's an exponential reduction compared to typical fixed-rate schemes. Numerical simulations validate the theoretical results, making this a practical step toward scalable, bandwidth-efficient distributed optimization for robotics, smart grids, and networked control systems.