ZEBRA: Zero-shot Budgeted Resource Allocation for LLM Orchestration

Efficient resource allocation is a critical capability for full autonomy in multi-agent systems. Existing tools typically provide indirect mechanisms for budget control, but do not optimize outcome quality under a fixed resource constraint. We introduce ZEBRA, a zero-shot budgeted resource allocation framework that models phase-level budget assignment as a continuous nonlinear knapsack problem. Rather than allocating budget directly, ZEBRA estimates phase utility curves and then computes the corresponding budget allocations algorithmically at inference time. We study two aggregations of phase utility -- an additive sum and a multiplicative product -- and unify them under a single dual-search solver. Through experiments on a balanced $150$-task APPS interview benchmark, both objectives outperform direct LLM allocation on every aggregate metric, and the gap scales with budget pressure: at $\alpha = 0.5$, ZEBRA retains $94.4\%$ of unconstrained quality versus $88.1\%$ for the LLM-direct baseline. These results suggest that lightweight algorithmic guidance -- without task-specific fine-tuning or reinforcement learning -- can improve the economic behavior of autonomous multi-agent systems.