# Literature Review: Cost-Aware Agent Routing

## What Exists

### Model Routing

**RouteLLM** (2406.18665, UC Berkeley/LMSYS, 2024): Trains BERT-based router on Chatbot Arena preference data. Achieves 2x+ cost reduction without sacrificing quality. Simple BERT classifier is surprisingly effective. Does NOT use execution feedback — routes based on input features only.

**HybridLLM** (2404.14618, 2024): Probabilistic router predicts Pr[H(x) ≥ 0] (quality gap favorable for small model). Uses BART score as quality proxy. 40% fewer calls to large model with no quality drop.

**CARROT** (SPROUT dataset, 2025): Multi-model routing benchmark with per-model scores and token counts across 13 models and 44K prompts. Provides ground truth for which model succeeds on which task.

### Cascade Inference

**Cascade Routing** (2410.10347, ETH SRI, ICLR 2025): Unifies routing (ex-ante) with cascading (post-hoc). Key finding: **quality estimators are the #1 factor**. Post-hoc estimates dramatically outperform ex-ante. Low σ_post benefits cascading; low σ_ante benefits routing. The combination wins.

**RouteNLP** (2604.23577, 2026): 3-component system: difficulty-aware router + confidence-calibrated cascading + distillation-routing co-optimization. Token-level uncertainty u(m,x) = (1/L)Σ(1 - p(y_i|x)) from softmax probabilities. Conformal risk control with α=0.05. **58% cost reduction in production** (5K queries/day).

**CP-Router** (2505.19970, 2025): Training-free uncertainty-aware routing between LLM and Large Reasoning Model. Uses entropy from cheap model output as escalation signal. No training required — just compute entropy and compare to conformal threshold.

### Agentic Routing

**BAAR** (2602.21227, 2025): Budget-Aware Agentic Routing via Boundary-Guided Training. Trains router (Qwen2.5-7B) to decide per-step which model to use. Two-phase training: BoSFT (difficulty taxonomy: Easy/Hard/Intractable) + BoPO (GRPO with boundary-relative rewards). Generalizes to strict per-task budget constraints.

**BEST-Route** (2506.22716, Microsoft, 2025): Generates best-of-n samples from cheap model, selects best via proxy reward model. Router predicts both model and number of samples n. Up to 60% cost reduction with <1% performance drop.

### Execution Feedback

**ClawTrace** (2604.23853): Per-step cost attribution in agent traces. TraceCard format with USD cost + token counts + redundancy flags. **Prune patches cut median cost 32%.**

**LLMRouterBench** (2601.07206): 400K instances, 21 datasets, 33 models. Finding: **Simple baselines often match complex routers.** Model complementarity is real but hard to exploit.

### Failure Prediction

**AgentRewardBench** (2504.08942): 1,302 web agent trajectories with expert success/side-effect/repetition labels across 5 benchmarks and 4 LLMs.

### Selective Verification

**Process Reward Models** (multiple): Train verifier to score intermediate steps. Use only when confidence is low or risk is high. Reduces verification cost by 70-90% while maintaining safety.

## What Is Useful

| Paper | Key Takeaway | Applied In ACO |
|-------|-------------|---------------|
| RouteNLP | Conformal cascading with token-level uncertainty | Execution-feedback router (module 4) |
| Cascade Routing | Post-hoc >> ex-ante quality estimates | v9 feedback escalation |
| BAAR | Per-step routing with difficulty taxonomy | Per-step router (module 3) |
| BEST-Route | Best-of-N cheap sampling + reward model | Planned next step |
| CP-Router | Training-free entropy-based escalation | Simple fallback router |
| ClawTrace | Per-step cost attribution | Telemetry schema |
| SPROUT | Multi-model eval data | v11 training data |

## What Is Overkill

- **Full agent simulation environments** (SciWorld, ALFWorld) — we don't need to simulate the entire agent, just route each step
- **GRPO-based RL training** (BAAR) — XGBoost with real data outperforms RL with synthetic data
- **Distillation-routing co-optimization** (RouteNLP) — we're not training task-specific models
- **Complex multi-stage pipelines** — simple cascade + feedback is 80% of the benefit

## What Is Missing

1. **Execution-feedback routing with real model logprobs** — all work uses simulated or API-provided logprobs
2. **Conformal calibration for agent routing** — no paper provides distribution-free quality guarantees
3. **Per-step routing with per-step training data** — BAAR routes per step but trains on task-level outcomes
4. **Cost-quality Pareto frontier construction** — no paper constructs the full frontier, only point comparisons
5. **Real agent benchmarks with cost data** — SWE-Router is the only dataset with real USD costs per task

## What To Implement First

1. **Execution-feedback escalation** (RouteNLP pattern) — highest ROI, validated in production
2. **Per-tier XGBoost with real data** (our v10/v11 approach) — simple, effective, requires real traces
3. **Per-step routing** (BAAR pattern) — significant savings from routing steps differently
4. **Conformal calibration** (CP-Router pattern) — safety guarantees without training
5. **Best-of-N cheap sampling** (BEST-Route pattern) — orthogonal improvement to routing

Priority: Execution feedback > Real data training > Per-step routing > Conformal calibration > Best-of-N