# Hierarchical Budget Policy Optimization for Adaptive Reasoning

arXiv: https://arxiv.org/abs/2507.15844 · HTML: https://mlsanity.com/paper/2507.15844/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 30 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 28 of 28)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [AdaCoT: Pareto-Optimal Adaptive Chain-of-Thought Triggering via Reinforcement Learning](https://mlsanity.com/paper/2505.11896/) (2025)
- [Think Only When You Need with Large Hybrid-Reasoning Models](https://mlsanity.com/paper/2505.14631/) (2025)
- [Learning When to Think: Shaping Adaptive Reasoning in R1-Style Models via Multi-Stage RL](https://mlsanity.com/paper/2505.10832/) (2025)
- [SelfBudgeter: Adaptive Token Allocation for Efficient LLM Reasoning](https://mlsanity.com/paper/2505.11274/) (2025)
- [ARM: Adaptive Reasoning Model](https://mlsanity.com/paper/2505.20258/) (2025)
- [ThinkSwitcher: When to Think Hard, When to Think Fast](https://mlsanity.com/paper/2505.14183/) (2025)
- [Scalable Chain of Thoughts via Elastic Reasoning](https://mlsanity.com/paper/2505.05315/) (2025)
- [ConCISE: Confidence-guided Compression in Step-by-step Efficient Reasoning](https://mlsanity.com/paper/2505.04881/) (2025)
- [When to Continue Thinking: Adaptive Thinking Mode Switching for Efficient Reasoning](https://mlsanity.com/paper/2505.15400/) (2025)
- [HAPO: Training Language Models to Reason Concisely via History-Aware Policy Optimization](https://mlsanity.com/paper/2505.11225/) (2025)
- [PATS: Process-Level Adaptive Thinking Mode Switching](https://mlsanity.com/paper/2505.19250/) (2025)

## Built on by (most cited first, 8 of 8)

- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [DART: Draft-Agreement Routing for Training-Free Adaptive Thinking Budgets in Hybrid Reasoning Models](https://mlsanity.com/paper/2606.23181/) (2026)
- [PVPO: Pre-Estimated Value-Based Policy Optimization for Agentic Reasoning](https://mlsanity.com/paper/2508.21104/) (2025)
- [Overthinking Reduction with Decoupled Rewards and Curriculum Data Scheduling](https://mlsanity.com/paper/2509.25827/) (2025)
- [Stepwise Penalization for Length-Efficient Chain-of-Thought Reasoning](https://mlsanity.com/paper/2603.00296/) (2026)
- [ZEBRA: Zero-shot Budgeted Resource Allocation for LLM Orchestration](https://mlsanity.com/paper/2605.20485/) (2026)
- [HMPO: Hybrid Median-length Policy Optimization for Chain-of-Thought Compression](https://mlsanity.com/paper/2606.01934/) (2026)
- [LIMBO: Lifelong Inference-Time Memory and Budget Optimization for LLM Agents](https://mlsanity.com/paper/2609.14138/) (2026)

## Abstract (arXiv)

Large reasoning models achieve remarkable performance through extensive chain-of-thought generation, yet they suffer from a critical inefficiency: applying uniformly extensive reasoning regardless of problem complexity. We present Hierarchical Budget Policy Optimization (HBPO), a reinforcement learning framework that enables models to learn problem-specific reasoning depths without sacrificing capability. Unlike existing approaches that impose rigid constraints or rely on discrete mode selection, HBPO partitions the exploration space into budget-constrained hierarchies (512-2560 tokens), each with differentiated reward structures that preserve both efficiency incentives and reasoning capabilities. This design addresses a fundamental challenge in efficient reasoning training: traditional length penalties systematically bias models away from necessary long reasoning paths, causing exploration space collapse. Through hierarchical sampling and budget-aware rewards, HBPO maintains exploration diversity while teaching models to recognize when extended deliberation is warranted. Extensive experiments demonstrate that HBPO reduces average token usage by up to 60.6% while improving accuracy by 3.14% across four reasoning benchmarks. Most notably, HBPO exhibits emergent adaptive behavior where models automatically adjust reasoning depth based on problem complexity. Our results suggest that reasoning efficiency and capability are not inherently conflicting, and can be simultaneously optimized through appropriately structured hierarchical training that preserves exploration diversity.