Cost-Aware Query Routing in RAG: Empirical Analysis of Retrieval Depth Tradeoffs

Agentic Retrieval-Augmented Generation (RAG) systems combine iterative search, planning prompts, and retrieval backends, but deployed settings impose explicit budgets on tool calls and completion tokens. We present a controlled measurement study of how search depth, retrieval strategy, and completion budget affect accuracy and cost under fixed constraints. Using Budget-Constrained Agentic Search (BCAS), a model-agnostic evaluation harness that surfaces remaining budget and gates tool use, we run comparisons across six LLMs and three question-answering benchmarks. Across models and datasets, accuracy improves with additional searches up to a small cap, hybrid lexical and dense retrieval with lightweight re-ranking produces the largest average gains in our ablation grid, and larger completion budgets are most helpful on HotpotQA-style synthesis. These results provide practical guidance for configuring budgeted agentic retrieval pipelines and are accompanied by reproducible prompts and evaluation settings.

Graph-based retrieval can improve multi-hop question answering, but existing approaches often incur high query-time costs and produce diffuse, oversized contexts that reduce generation efficiency. We present LiteRAG, a graph-based retrieval method that replaces expensive retrieval-time LLM control with query-conditioned algorithmic exploration and reasoning-chain context construction. On DistComp, a benchmark for multi-hop retrieval over distributed-systems papers, LiteRAG attains the highest overall quality among the evaluated methods (0.798) while reducing per-query latency by over 100$\times$ and cost by over 99% relative to GraphRAG Global and DRIFT. On UltraDomain, it matches LinearRAG on overall quality while using about 14$\times$ fewer tokens. An ablation study indicates that LiteRAG's query-adaptive thresholding and community-aware hub penalization are the main drivers of its token-efficiency gains.

Retrieval-augmented generation (RAG) typically retrieves a fixed number of passages for every query. This is wasteful when the reader already knows the answer, and it can be harmful when irrelevant or partially relevant passages distract the reader. We formulate adaptive RAG as calibrated retrieval-budget allocation: given a query, decide whether to answer closed-book, retrieve a compact context (k=1), retrieve a full context (k=5), or abstain. The contribution is a probability interface rather than a new raw uncertainty signal. We calibrate sequence log-probability and prefix-logit uncertainty signals into probabilities of correctness, then use these probabilities for graded context selection, selective abstention, and explicit latency/token trade-offs. Across core QA experiments on TriviaQA, Natural Questions, and MS MARCO, with auxiliary PopQA motivation and Qwen/Llama family checks, diagnostic out-of-fold calibration improves probability quality dramatically: for sequence log-probability, ECE drops from 0.275 to 0.062 on TriviaQA, 0.643 to 0.009 on NQ, and 0.711 to 0.031 on MS MARCO. Graded retrieval improves full-context and passage-budget frontiers for both our signal and TARG-style prefix entropy/margin, while retrieval-call AUC remains essentially tied with binary gating because k=1 is still a retrieval call. Held-out train/validation/test threshold experiments report deployable operating points. At matched-accuracy frontier operating points, a measured cost model reveals that gating is not universally faster: it increases latency by about 27% on Qwen3-8B but saves about 8% on Qwen3-32B. These results support a nuanced view of adaptive RAG: calibrated confidence is best understood as a reusable interface for allocating retrieval budget under task and system constraints.