Thinking Forward and Backward: Multi-Objective Reinforcement Learning for Retrieval-Augmented Reasoning

Retrieval-augmented generation (RAG) has proven to be effective in mitigating hallucinations in large language models, yet its effectiveness remains limited in complex, multi-step reasoning scenarios. Recent efforts have incorporated search-based interactions into RAG, enabling iterative reasoning with real-time retrieval. Most approaches rely on outcome-based supervision, offering no explicit guidance for intermediate steps. This often leads to reward hacking and degraded response quality. We propose Bi-RAR, a novel retrieval-augmented reasoning framework that evaluates each intermediate step jointly in both forward and backward directions. To assess the information completeness of each step, we introduce a bidirectional information distance grounded in Kolmogorov complexity, approximated via language model generation probabilities. This quantification measures both how far the current reasoning is from the answer and how well it addresses the question. To optimize reasoning under these bidirectional signals, we adopt a multi-objective reinforcement learning framework with a cascading reward structure that emphasizes early trajectory alignment. Empirical results on seven question answering benchmarks demonstrate that Bi-RAR surpasses previous methods and enables efficient interaction and reasoning with the search engine during training and inference.

Generative Retrieval as Multi-Vector Dense Retrieval

Generative retrieval generates identifiers of relevant documents in an end-to-end manner using a sequence-to-sequence architecture for a given query. The relation between generative retrieval and other retrieval methods, especially those based on matching within dense retrieval models, is not yet fully comprehended. Prior work has demonstrated that generative retrieval with atomic identifiers is equivalent to single-vector dense retrieval. Accordingly, generative retrieval exhibits behavior analogous to hierarchical search within a tree index in dense retrieval when using hierarchical semantic identifiers. However, prior work focuses solely on the retrieval stage without considering the deep interactions within the decoder of generative retrieval. In this paper, we fill this gap by demonstrating that generative retrieval and multi-vector dense retrieval share the same framework for measuring the relevance to a query of a document. Specifically, we examine the attention layer and prediction head of generative retrieval, revealing that generative retrieval can be understood as a special case of multi-vector dense retrieval. Both methods compute relevance as a sum of products of query and document vectors and an alignment matrix. We then explore how generative retrieval applies this framework, employing distinct strategies for computing document token vectors and the alignment matrix. We have conducted experiments to verify our conclusions and show that both paradigms exhibit commonalities of term matching in their alignment matrix.