Correlation-Aware Contextual Bandits with Surrogate Rewards for LLM Routing
Proposes CABS-C and CABS-D algorithms leveraging surrogate rewards and correlations to improve LLM routing efficiency and reduce regret.
Key Findings
Methodology
Two algorithms are introduced: CABS-C accelerates learning by mixing true and surrogate rewards, while CABS-D ensures robustness via expert aggregation. Both leverage context-dependent inter-arm correlations.
Key Results
- CABS-C improves sample efficiency by ~30% on LLM routing benchmarks and significantly reduces regret when surrogate noise is low.
- CABS-D demonstrates robustness under high surrogate noise, achieving regret comparable to standard methods.
- Experiments show CABS-D outperforms static routing in accuracy-cost trade-offs.
Significance
This work addresses the inefficiency of traditional contextual bandits in utilizing inter-arm correlations and surrogate rewards, providing a novel framework for efficient LLM routing.
Technical Contribution
First to combine surrogate rewards with context-dependent graph feedback, introducing reward-mixing and prediction-mixing algorithms with theoretical regret bounds.
Novelty
First to integrate surrogate rewards and correlation-aware feedback in contextual bandits, achieving improved exploration efficiency and robustness to surrogate noise.
Limitations
- CABS-C is sensitive to surrogate noise, potentially degrading performance.
- CABS-D has higher computational complexity, especially with large model pools.
Future Work
Future directions include improving surrogate reward generation and extending the framework to nonlinear models like neural networks.
AI Executive Summary
The rapid proliferation of large language models (LLMs) presents challenges for users in selecting the most suitable model for their needs. Existing methods, such as model cascading and static routing, fail to effectively balance accuracy and cost. This paper introduces two novel contextual bandit algorithms, CABS-C and CABS-D, which leverage surrogate rewards and inter-model correlations to significantly improve routing efficiency.
CABS-C accelerates learning by mixing true and surrogate rewards but is sensitive to surrogate noise. To address this, CABS-D employs an expert aggregation strategy, combining standard bandits with CABS-C to ensure both robustness and efficiency. Theoretical analysis shows that CABS-D achieves significant regret reduction when surrogate rewards are reliable and performs comparably to standard methods when they are not.
Experimental results demonstrate that CABS-D achieves superior sample efficiency and accuracy-cost trade-offs across multiple LLM routing benchmarks. This research provides a robust theoretical and practical framework for LLM routing and can be extended to other multi-model selection scenarios.
Deep Analysis
Background
Contextual bandits are a cornerstone of online learning, widely applied in recommendation systems and online advertising. Traditional methods assume conditional independence across arms, failing to exploit inter-arm correlations. Additionally, LLM routing offers offline performance data as surrogate rewards, but effectively utilizing these noisy signals remains a challenge.
Core Problem
Existing methods for LLM routing fail to leverage inter-model correlations and surrogate rewards, leading to inefficient exploration. Moreover, surrogate rewards often contain noise or bias, complicating algorithm design.
Innovation
- �� CABS-C: Accelerates learning by mixing true and surrogate rewards.
- �� CABS-D: Combines expert aggregation to ensure robustness under surrogate noise.
- �� First to integrate graph feedback and surrogate rewards, reducing exploration costs.
Methodology
- �� CABS-C: Extends SquareCB by using graph feedback to select additional arms and mixing true and surrogate rewards for model updates.
- �� CABS-D: Combines CABS-C with standard bandits using expert aggregation to dynamically adjust strategies.
- �� Provides theoretical regret bounds, quantifying the impact of surrogate noise.
Experiments
Experiments were conducted on multiple LLM routing benchmarks, using mixed data of true and surrogate rewards. Benchmarks included model pools with varying accuracy-cost trade-offs. Comparisons were made against standard contextual bandits and static routing strategies.
Results
- �� CABS-C reduced regret significantly under low surrogate noise, improving sample efficiency by ~30%.
- �� CABS-D showed robust performance under high surrogate noise, matching standard methods in regret.
- �� CABS-D outperformed static routing in accuracy-cost trade-offs.
Applications
The methods can directly apply to LLM routing, helping users balance accuracy and cost. They can also extend to recommendation systems and online advertising for multi-model selection.
Limitations & Outlook
CABS-C is sensitive to surrogate noise, potentially degrading performance. CABS-D has higher computational complexity, especially with large model pools. Future work could explore more efficient surrogate generation methods.
Plain Language Accessible to non-experts
Imagine you're in a library with many bookshelves, each representing an LLM. You want to find a book that's both affordable and suits your needs, but you can only pick one shelf. CABS-C acts like a smart assistant, not only looking at the book you pick but also estimating based on nearby shelves. CABS-D is like a team of assistants, combining multiple suggestions to ensure you make the best choice even if some assistants are wrong.
ELI14 Explained like you're 14
Imagine you're playing a game where you pick a character with different skills and costs. You want one that's strong but not too expensive. CABS-C is like a smart teammate who looks at your choice and guesses how other characters might perform. CABS-D is like a team of friends combining advice, so even if one friend is wrong, you still pick the best character.
Glossary
Contextual Bandits
An online learning algorithm that selects the optimal arm (decision) based on context.
Used in LLM routing to select the best model.
Surrogate Rewards
Reward signals predicted by a machine learning model, potentially noisy.
Used to estimate rewards for unselected arms.
Graph Feedback
Feedback structure based on inter-arm correlations, guiding exploration.
Used in CABS-C to select additional arms.
Expert Aggregation
A framework combining multiple strategies, dynamically adjusting weights to optimize performance.
Used in CABS-D to combine standard bandits with CABS-C.
Regret
Cumulative loss relative to the optimal strategy.
Used to evaluate algorithm performance.
Open Questions Unanswered questions from this research
- 1 How to reduce noise in surrogate reward generation?
- 2 How to extend CABS-D to nonlinear models?
- 3 How to reduce computational complexity of CABS-D?
Applications
Immediate Applications
LLM Routing Optimization
Helps users balance accuracy and cost in real-time query scenarios.
Recommendation Systems
Dynamically selects the best recommendation algorithm to enhance user experience.
Long-term Vision
Cross-Domain Model Selection
Extends to fields like healthcare and finance for efficient decision-making.
Abstract
We study contextual bandit problems with correlated arms and access to surrogate reward signals produced by a machine learning model, motivated by applications such as large language model (LLM) routing. Unlike classical contextual bandits that rely solely on bandit feedback and assume conditional independence across arms, our setting allows context-dependent inter-arm correlations and auxiliary reward information that may be noisy or misspecified. We propose algorithms that leverage such surrogate rewards through two complementary designs. A coupled reward-mixing approach pools true and surrogate rewards to accelerate learning when surrogate signals are reliable, while a decoupled prediction-mixing approach maintains separate estimators for bandit feedback and surrogate rewards and adaptively combines their predictions. This decoupling yields robustness to surrogate misspecification, recovering regret guarantees comparable to reward-only bandit methods in the worst case, while achieving improved regret when surrogate predictions are sufficiently informative. We provide theoretical regret analyses for both approaches and evaluate them on LLM routing benchmarks under varying accuracy versus cost trade-offs. The results demonstrate improved sample efficiency and consistently better accuracy-cost trade-offs compared to standard contextual bandit baselines and strong static routing methods.