A Unified Approach to Routing and Cascading for LLMs

TL;DR

This paper introduces a unified, theoretically optimal framework called cascade routing that combines routing and cascading strategies for large language models, improving cost-performance tradeoffs in model selection.

Contribution

It derives a formal optimal strategy for cascading, proves the optimality of routing, and proposes a unified approach that outperforms existing methods in model selection for LLMs.

Findings

Cascade routing outperforms individual strategies significantly.

Good quality estimators are crucial for effective model selection.

The framework identifies when routing or cascading are most beneficial.

Abstract

The availability of a wide range of large language models (LLMs) embedded in various agentic systems has significantly increased the potential of model selection strategies to improve the cost-performance tradeoff. Existing strategies involve either routing, where a single model is chosen per query, or cascading, which sequentially runs increasingly larger models until a satisfactory answer is found. However, current approaches face three key limitations: they (1) lack formal proofs of optimality, (2) fail to identify the conditions under which these strategies are most effective to improve the cost-performance tradeoff, and (3) are unable to combine both paradigms for further improvements. To address these issues, we first derive a novel optimal strategy for cascading and prove the optimality of an existing routing strategy. Further, we propose cascade routing, a unified framework that integrates routing and cascading into a theoretically optimal strategy. Through our analysis, we identify good quality estimators as the critical factor for the success of model selection paradigms. Finally, in our experiments, we show that cascade routing consistently outperforms the individual approaches by a large margin and we analyze quality estimators to determine when routing and/or cascading are useful paradigms for model selection.