BALAR : A Bayesian Agentic Loop for Active Reasoning

Large language models increasingly operate in interactive settings where solving a task requires multiple rounds of information exchange with a user. However, most current systems treat dialogue reactively and lack a principled mechanism to reason about what information is missing. We propose BALAR (Bayesian Agentic Loop for Active Reasoning), a task-agnostic outer-loop algorithm that requires no fine-tuning and enables multi-turn interaction between an LLM agent and a user. BALAR maintains a structured belief over latent states, selects clarifying questions by maximizing expected mutual information, and dynamically expands its state representation when the current one proves insufficient. We evaluate BALAR on three diverse benchmarks: AR-Bench-DC (detective cases), AR-Bench-SP (thinking puzzles), and iCraft-MD (clinical diagnosis). BALAR outperforms all baselines across the three benchmarks, with 14.6% higher accuracy on AR-Bench-DC, 38.5% on AR-Bench-SP, and 30.5% on iCraft-MD. We further study whether BALAR can serve as a teacher for a questioning policy through supervised fine-tuning (SFT), direct preference optimization (DPO), and dense-reward reinforcement learning (RL). Across 18 iCraft-MD replications, distilling BALAR into a Llama-8B yields relative gains in frozen-Qwen final-answer accuracy of 8.1% with SFT, 10.9% with DPO, and 12.1% with RL over the untuned policy.