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DAPO : Improving Multi-Step Reasoning Abilities of Large Language Models with Direct Advantage-Based Policy Optimization
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Proposes DAPO, an offline step-level RL method that trains a value critic on Monte Carlo completion estimates and then optimizes the LLM policy with a squared-loss advantage-regression objective, evaluated on math and code benchmarks.
Problem
Sparse terminal rewards and instability of actor-critic methods (PPO) when improving multi-step reasoning in LLMs, with high sampling cost for on-policy RL.
Approach
Trains a step-level critic separately (BCE on MC estimates of success probability) and then fits the policy offline to critic-estimated advantages via a squared loss derived from KL-regularized step-level RL, avoiding co-training of actor and critic.
Key results
- Skywork-Math-LLama improves on MATH from 41.90 to 46.88 after one DAPO iteration and 50.54 after iteration 2.
- Qwen2.5-Math-7B-Instruct improves on MATH from 83.42 to 84.86 with DAPO.
- META-LLama-3.1-8B-Instruct gains +3.0 on HumanEval and +9.2 on MBPP+ but OpenO1-LLama-8B-v0.1 drops 2.4 on LiveCodeBench.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply DAPO | Qwen2.5-72B-Instruct · MATH | accuracy: 82.90 -> 84.70 | Helped |
| Apply DAPO | Qwen2.5-Math-7B-Instruct · GSM8K | accuracy: 95.78 -> 96.14 | Helped |
| Apply DAPO | Qwen2.5-72B-Instruct · Minerva Math | accuracy: 46.30 -> 50.00 | Helped |
| Apply DAPO | Qwen2.5-72B-Instruct · Olympiad Bench | accuracy: 45.45 -> 47.70 | Helped |
| Apply DAPO | Qwen2.5-72B-Instruct · College Math | accuracy: 43.00 -> 43.40 | Helped |
| Apply DAPO | META-Llama-3.1-8B-Instruct · HumanEval | accuracy: 72.0 -> 75.0 | Helped |
| Apply DAPO | META-Llama-3.1-8B-Instruct · HumanEval+ | accuracy: 66.5 -> 68.9 | Helped |
| Apply DAPO | META-Llama-3.1-8B-Instruct · MBPP | accuracy: 72.0 -> 77.0 | Helped |
| Apply DAPO | META-Llama-3.1-8B-Instruct · MBPP+ | accuracy: 56.9 -> 66.1 | Helped |
| Apply DAPO | META-Llama-3.1-8B-Instruct · LiveCodeBench | accuracy: 18.8 -> 20.9 | Helped |
| Apply DAPO | OpenO1-Llama-8B-v0.1 · LiveCodeBench | accuracy: 16.1 -> 13.7 (-2.4) | Hurt |
| Apply DAPO | META-Llama-3.1-8B-Instruct · Minerva Math | accuracy: 26.48 -> 23.54 (-2.94) | Hurt |
Surprising findings
- DAPO decreases performance on some out-of-domain benchmarks, e.g., Minerva MATH for META-LLama-3.1-8B-Instruct (-2.94) and Qwen2-Math-7B-Instruct (-2.56).
- The critic is deliberately treated as a value function rather than a process reward model, arguing that using it as a reward risks reward hacking on step count.
Limitations
- Only a small number of training queries (7500 MATH, ~4000 TACO) used; scaling behavior unexplored.
- Iterative DAPO only tested on two models and two iterations due to compute limits.
- Computational cost of the full pipeline is high.
Experimental setup
Datasets: MATH TACO
Benchmarks: MATH GSM8K Minerva Math OlympiadBench College Math HumanEval HumanEval+ MBPP MBPP+ LiveCodeBench
Metrics: greedy accuracy (pass@1, zero-shot, temperature 0)
Baselines: Qwen2.5-Math-7B-Instruct Qwen2-Math-7B-Instruct Skywork-O1-Open-LLama3.1-8B META-LLama-3.1-8B-Instruct OpenO1-LLama-8B-v0.1
Builds on: DPO DRO PPO GRPO Step-DPO
Closest papers by meaning
- DAPO: An Open-Source LLM Reinforcement Learning System at Scale (NeurIPS 2025 · similarity 0.91)
- Accelerating RL for LLM Reasoning with Optimal Advantage Regression (NeurIPS 2025 · similarity 0.91)
- Advancing LLM Reasoning with Natural Language and Numerical Feedback (ICML 2026 · similarity 0.91)
- Agentic Reinforced Policy Optimization (ICLR 2026 · similarity 0.90)
- Diversity-Aware Policy Optimization for Large Language Model Reasoning (NeurIPS 2025 · similarity 0.89)
- d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning (NeurIPS 2025 · similarity 0.89)
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