A bi-objective $\epsilon$-constrained framework for quality-cost optimization in language model ensembles

We propose an ensembling framework that uses diverse open-sourced Large Language Models (LLMs) to achieve high response quality while maintaining cost efficiency. We formulate a bi-objective optimization problem to represent the quality-cost tradeoff and then introduce an additional budget constraint that reduces the problem to a straightforward 0/1 knapsack problem. We empirically demonstrate that our framework outperforms the existing ensembling approaches in response quality while significantly reducing costs.