Direction-Aware Iterative Graph Retrieval via Online Convex Optimization for Long-Document Multi-Hop Question Answering

Long-document multi-hop question answering requires retrieving evidence whose relevance may become apparent only after intermediate reasoning steps. Graph-based retrieval can connect such evidence, but diffusion from a fixed seed distribution may assign limited probability mass to distant evidence or disperse it across competing outgoing edges. We propose RCT-PPR, an iterative retrieval framework that adapts both the restart distribution and local transition probabilities of Personalized PageRank. An LLM controller identifies new seed entities and a semantic target direction from the retrieved context. The target induces a linear alignment loss over each node’s outgoing probability simplex, enabling a multiplicative-weights update that preserves normalized transitions and accumulates semantic feedback across iterations. We characterize the cumulative alignment loss of this update through a local static-regret bound against the best fixed outgoing distribution in hindsight. On three multi-hop QA datasets from LongBench, RCT-PPR achieves 53.3 average F1, exceeding HippoRAG 2 by 6.4 points. Ablations reduce average F1 to 48.1 with a single retrieval round and to 51.3 without the OCO-based update, supporting the contributions of iterative retrieval and transition adaptation.