# Direct Diversity Optimization for Diverse Successful Trajectories in Preference Post-Training

arXiv: https://arxiv.org/abs/2609.10052 · HTML: https://mlsanity.com/paper/2609.10052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [Does Writing with Language Models Reduce Content Diversity?](https://mlsanity.com/paper/2309.05196/) (2023)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [Chain of Preference Optimization: Improving Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2406.09136/) (2024)
- [Watch Every Step! LLM Agent Learning via Iterative Step-Level Process Refinement](https://mlsanity.com/paper/2406.11176/) (2024)
- [AgentPRM: Process Reward Models for LLM Agents via Step-Wise Promise and Progress](https://mlsanity.com/paper/2511.08325/) (2025)
- [Diversity Policy Gradient for Sample Efficient Quality-Diversity Optimization](https://mlsanity.com/paper/2006.08505/) (2020)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Diverse Preference Learning for Capabilities and Alignment](https://mlsanity.com/paper/2511.08594/) (2025)
- [Baba Is AI: Break the Rules to Beat the Benchmark](https://mlsanity.com/paper/2407.13729/) (2024)
- [On Extending Direct Preference Optimization to Accommodate Ties](https://mlsanity.com/paper/2409.17431/) (2024)

## Abstract (arXiv)

LLM agents for sequential decision tasks are often post-trained with trajectory-level outcome labels, but such labels provide little supervision for preserving multiple successful branches from the same decision state. We study this problem as successful strategy coverage: how broadly a model realizes distinct successful strategies under a fixed rollout budget. We present Direct Diversity Optimization (DDO), an offline post-training method that combines Divergence-Tree Collection (DTC) with the Reference-Relative Target-Odds Objective (RTO). DTC constructs state-aligned branch sets rooted at shared decision states, and RTO trains the model to match reference-relative targets over successful alternatives. DDO achieves the strongest task success and successful strategy coverage among the compared post-training methods across BabyAI, BabaIsAI, and WebShop. It also achieves the highest recovery rate after local action replacement and higher task success and coverage than successful-only imitation and decoding-time diversification controls.