# OPTS-TTPO: Enhancing Finite-Sample Policy-Gradient Learning with Tree Search

arXiv: https://arxiv.org/abs/2609.40035 · HTML: https://mlsanity.com/paper/2609.40035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 60 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 44)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [Self-Imitation Learning](https://mlsanity.com/paper/1806.05635/) (2018)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Tree Search for LLM Agent Reinforcement Learning](https://mlsanity.com/paper/2509.21240/) (2025)
- [Learning and Planning in Complex Action Spaces](https://mlsanity.com/paper/2104.06303/) (2021)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [Monte-Carlo Tree Search as Regularized Policy Optimization](https://mlsanity.com/paper/2007.12509/) (2020)
- [TreePO: Bridging the Gap of Policy Optimization and Efficacy and Inference Efficiency with Heuristic Tree-based Modeling](https://mlsanity.com/paper/2508.17445/) (2025)
- [TreeRPO: Tree Relative Policy Optimization](https://mlsanity.com/paper/2506.05183/) (2025)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [TreeGRPO: Tree-Advantage GRPO for Online RL Post-Training of Diffusion Models](https://mlsanity.com/paper/2512.08153/) (2025)

## Abstract (arXiv)

The policy-gradient theorem gives the exact gradient under the current policy, but finite on-policy samples may miss rare high-return trajectories. We study whether tree search improves their coverage within a fixed budget while controlling gradient bias. We introduce On-Policy Parallel Tree Search (OPTS) and Tree Trajectory Policy Optimization (TTPO) using on-policy tree trajectories, which sample new suffixes from the current policy at visited states. This needs no action-distribution correction, although branching changes state visitation. Our Branch Aggregation Lemma shows that branch-weighted tree statistics recover chain expectations when branch choices and weights are fixed before outgoing transitions are sampled. OPTS selects expansion states using estimated performance differences. Under deterministic dynamics, exact values, and max-backup advantages, the induced search policy's expected return improves monotonically with the budget. We bound the gradient bias from adaptive expansion and show that max backup assigns prefix credit to actions leading to better discovered suffixes. Against a finite chain reference, TTPG's measured bias stays near its no-branching level, while NaivePG's bias grows from 0.1251 to 0.4884. At matched budgets, reward- and value-guided OPTS improve correct-answer coverage and majority-vote accuracy over independent sampling. At matched branch counts, OPTS + TTPG gains coverage with a modest bias increase relative to Fixed-branch + TTPG. Under matched interaction or rollout budgets, OPTS-TTPO improves MuJoCo tail returns over PPO by up to 28.6%, achieves a 34-22-1 win-loss-tie record against PPO on Atari-57 under the last-100-log mean-return metric, and improves micro-averaged avg@32 and pass@32 over PPO across all four Qwen3 models.