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Causal LLM Routing: End-to-End Regret Minimization from Observational Data
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Proposes a causal end-to-end LLM routing framework that learns routing policies by minimizing decision regret from observational (single-model feedback) data, with classification and softmax-weighted regret surrogates and an interval-conditioned router for heterogeneous cost preferences.
Problem
LLM routing typically relies on full-feedback data and decoupled metric prediction, which compounds errors and ignores treatment bias when only the deployed model's outcome is observed.
Approach
Learns routing directly by minimizing regret under a doubly robust counterfactual utility estimate, using a cross-entropy upper bound and a softmax-weighted regret surrogate, plus an interval-conditioned joint router that interpolates between two endpoint cost-sensitivity models.
Key results
- On SPROUT with BERT embeddings, RM-Softmax reaches 84.97 utility at lambda=0 vs 83.34 for R&C and 66.88 for the decoupled Baseline, averaged over 10 trials.
- RM-Softmax attains the highest average AUC on all four dataset/embedding settings (e.g., 0.3320 on SP-BERT vs 0.1642 for Causal-CARROT kNN).
- RM-Interval generalizes to unseen odd lambda values, often matching or exceeding models trained directly at those values.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RM-Softmax instead of the strongest non-proposed method, Full-Feedback | LLM routing · RouterBench, BERT embeddings | AUC: 0.1839 -> 0.2286 | Helped |
| Use RM-Softmax instead of the strongest non-proposed method, Full-Feedback | LLM routing · RouterBench, LLaMA-3.2-1B embeddings | AUC: 0.1719 -> 0.2213 | Helped |
| Use RM-Softmax instead of the strongest non-proposed method, Causal-CARROT (kNN) | LLM routing · SPROUT, BERT embeddings | AUC: 0.1642 -> 0.3320 | Helped |
| Use RM-Interval instead of the strongest non-proposed method, Full-Feedback | LLM routing · SPROUT, LLaMA-3.2-1B embeddings | AUC: 0.1655 -> 0.2464 | Helped |
| Account for treatment bias using causal correction instead of the uncorrected Baseline | LLM routing · RouterBench, BERT embeddings | AUC: 0.0890 -> 0.1539 | Helped |
| Account for treatment bias using causal correction instead of the uncorrected Baseline | LLM routing · RouterBench, LLaMA-3.2-1B embeddings | AUC: 0.0134 -> 0.1433 | Helped |
| Account for treatment bias using causal correction instead of the uncorrected Baseline | LLM routing · SPROUT, BERT embeddings | AUC: 0.0255 -> 0.1642 | Helped |
| Account for treatment bias using causal correction instead of the uncorrected Baseline | LLM routing · SPROUT, LLaMA-3.2-1B embeddings | AUC: 0.0148 -> 0.1618 | Helped |
| Optimize regret end-to-end with RM-Softmax instead of two-stage CF-Regression | LLM routing · RouterBench, BERT embeddings | AUC: 0.1412 -> 0.2286 | Helped |
| Optimize regret end-to-end with RM-Softmax instead of two-stage CF-Regression | LLM routing · RouterBench, LLaMA-3.2-1B embeddings | AUC: 0.1119 -> 0.2213 | Helped |
| Optimize regret end-to-end with RM-Softmax instead of two-stage CF-Regression | LLM routing · SPROUT, BERT embeddings | AUC: 0.1352 -> 0.3320 | Helped |
| Optimize regret end-to-end with RM-Softmax instead of two-stage CF-Regression | LLM routing · SPROUT, LLaMA-3.2-1B embeddings | AUC: 0.1233 -> 0.2444 | Helped |
Surprising findings
- The decoupled Baseline performs far worse than even simple causal corrections, with AUC on RB-LLaMa of 0.0134 vs 0.1108 for R&C.
- Causal-CARROT EmbedNet underperforms its kNN variant substantially, especially at higher lambda values.
Limitations
- Observational data is simulated from full-feedback datasets rather than collected from real deployments.
- Theoretical guarantees rely on assumptions such as Lipschitz utilities and accurate endpoint models; the softmax surrogate proof is heuristic.
- Evaluation limited to two benchmarks and small embedding models (BERT-base, Llama-3.2-1B).
Experimental setup
Datasets: RouterBench SPROUT
Benchmarks: RouterBench SPROUT
Metrics: utility (accuracy minus lambda times cost) AUC of accuracy-cost curve
Baselines: Full-Feedback Baseline (CARROT-style decoupled) Regress-and-Compare Causal-CARROT (kNN) Causal-CARROT (EmbedNet) CF-Regression RouteLLM RoRF
Builds on: CARROT doubly robust estimator potential outcomes framework
Closest papers by meaning
- BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute (ICML 2025 · similarity 0.89)
- Lookahead Routing for Large Language Models (NeurIPS 2025 · similarity 0.88)
- RouteLLM: Learning to Route LLMs from Preference Data (ICLR 2025 · similarity 0.88)
- Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning (NeurIPS 2025 · similarity 0.88)
- A Unified Approach to Routing and Cascading for LLMs (ICML 2025 · similarity 0.88)
- Models Under SCOPE: Scalable and Controllable Routing via Pre-hoc Reasoning (ICML 2026 · similarity 0.87)
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