Budgeted Multi-Agent Routing: Adaptive Role Assignment and Communication Compression for Efficient LLM-Agent Collaboration

Multi-agent collaboration using large language mod els (LLMs) has shown promise in complex reasoning tasks, yet cu rrent approaches suffer from high computational costs, redundan t communication, and unstable performance gains. We propose B udgeted Multi-Agent Routing (BMAR), a framework that dynami cally allocates agents and communication rounds under explicit b udget constraints. BMAR introduces three key innovations: (1) ad aptive role assignment based on task characteristics and uncertai nty, (2) claim-evidence compression to reduce communication ove rhead, and (3) budget-aware routing that optimizes the accuracycost trade-off. Experiments across mathematical reasoning, multi -hop question answering, and code debugging demonstrate that $\mathbf{B}$ MAR achieves superior Pareto efficiency: at a $4 \times$ budget, BMAR improves accuracy by 8.9 percentage points on GSM8K over sing le-agent baselines (77.1% vs. 68.2%), while using 58% fewer toke ns than fixed multi-agent approaches at comparable accuracy lev els. Our approach provides a principled framework for deploying cost-effective multi-agent systems in resource-constrained enviro nments.