To evaluate ranked retrieval outputs in a RAG (Retrieval-Augmented Generation) system using nDCG (normalized discounted cumulative gain), you first need to assess how well the retriever orders documents by relevance, as the generator’s output often depends on this order. nDCG is ideal here because it quantifies the quality of a ranking by considering both the relevance of documents and their positions. For example, if a critical document for answering a query appears lower in the list, the generator might overlook it, leading to an incorrect or incomplete response. By applying nDCG, you assign higher scores to rankings where the most relevant documents appear earlier, reflecting their potential impact on the generator’s output. This directly aligns with RAG’s dependency on retrieval quality, as even a highly relevant document at position 5 may contribute less if the generator truncates or underweights later entries.
Implementing nDCG in RAG involves three steps. First, define relevance grades (e.g., 0 for irrelevant, 2 for highly relevant) for retrieved documents relative to a query. Second, compute the Discounted Cumulative Gain (DCG) by summing the relevance scores, with each score divided by a logarithmic discount based on its position. For instance, a document with relevance 2 at position 1 contributes 2, while the same document at position 3 contributes 2 / log₂(3+1) ≈ 1.0. Finally, normalize the DCG by comparing it to the ideal ranking (IDCG), which is the maximum possible DCG for that query. For example, if your RAG system retrieves documents ordered [2, 1, 3] (with relevance scores 3, 2, 1), but the ideal order is [3, 2, 1], nDCG would penalize the suboptimal positioning of the most relevant document (score 3). This process highlights whether the retriever’s ranking aligns with what the generator needs to produce accurate outputs.
However, there are practical considerations. nDCG requires human-annotated relevance labels, which can be time-consuming to obtain. In RAG, you might use synthetic labels (e.g., similarity scores between query and documents) as proxies, though this risks misalignment with true relevance. Additionally, nDCG focuses on retrieval quality, so it should complement, not replace, metrics evaluating the generator (e.g., BLEU, ROUGE, or task-specific accuracy). For example, if a medical RAG system retrieves a critical study at position 3 instead of 1, nDCG would reflect the ranking error, while the generator’s failure to use that study would require separate evaluation. By combining nDCG with end-to-end metrics, developers can isolate whether poor performance stems from retrieval or generation, enabling targeted improvements.