# KL-Regularized Reinforcement Learning is Designed to Mode Collapse

arXiv: https://arxiv.org/abs/2510.20817 · HTML: https://mlsanity.com/paper/2510.20817/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 58 of its 82 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 58)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Molecular De Novo Design through Deep Reinforcement Learning](https://mlsanity.com/paper/1704.07555/) (2017)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization](https://mlsanity.com/paper/2206.12411/) (2022)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Aligning Language Models with Preferences through f-divergence Minimization](https://mlsanity.com/paper/2302.08215/) (2023)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Molecule Edit Graph Attention Network: Modeling Chemical Reactions as Sequences of Graph Edits](https://mlsanity.com/paper/2006.15426/) (2020)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgetting](https://mlsanity.com/paper/2206.00761/) (2022)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)

## Built on by (most cited first, 30 of 31)

- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [A Comedy of Estimators: On KL Regularization in RL Training of LLMs](https://mlsanity.com/paper/2512.21852/) (2025)
- [GARDO: Reinforcing Diffusion Models without Reward Hacking](https://mlsanity.com/paper/2512.24138/) (2025)
- [Data-regularized Reinforcement Learning for Diffusion Models at Scale](https://mlsanity.com/paper/2512.04332/) (2025)
- [Where does output diversity collapse in post-training?](https://mlsanity.com/paper/2604.16027/) (2026)
- [On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity](https://mlsanity.com/paper/2606.26091/) (2026)
- [Vector Policy Optimization: Training for Diversity Improves Test-Time Search](https://mlsanity.com/paper/2605.22817/) (2026)
- [RPiAE: A Representation-Pivoted Autoencoder Enhancing Both Image Generation and Editing](https://mlsanity.com/paper/2603.19206/) (2026)
- [One Frozen Simulator Is Not Enough: Simulator Collapse in Multi-Agent RL](https://mlsanity.com/paper/2608.12253/) (2026)
- [Expected Return Causes Outcome-Level Mode Collapse in Reinforcement Learning and How to Fix It with Inverse Probability Scaling](https://mlsanity.com/paper/2601.21669/) (2026)
- [Poly-EPO: Training Exploratory Reasoning Models](https://mlsanity.com/paper/2604.17654/) (2026)
- [From Flow to One Step: Real-Time Multi-Modal Trajectory Policies via Implicit Maximum Likelihood Estimation-based Distribution Distillation](https://mlsanity.com/paper/2603.09415/) (2026)
- [Alignment Makes Language Models Normative, Not Descriptive](https://mlsanity.com/paper/2603.17218/) (2026)
- [TMPO: Trajectory Matching Policy Optimization for Diverse and Efficient Diffusion Alignment](https://mlsanity.com/paper/2605.10983/) (2026)
- [Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation](https://mlsanity.com/paper/2607.27372/) (2026)
- [Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability](https://mlsanity.com/paper/2605.09214/) (2026)
- [SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs](https://mlsanity.com/paper/2605.18864/) (2026)
- [Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier](https://mlsanity.com/paper/2606.18284/) (2026)
- [The One-Word Census: Answer-Choice Conformity Across 105 Language Models](https://mlsanity.com/paper/2607.12796/) (2026)
- [Tail-Likelihood Reinforcement Learning](https://mlsanity.com/paper/2609.02987/) (2026)
- [Policy Improvement Reinforcement Learning](https://mlsanity.com/paper/2604.00860/) (2026)
- [Multi2: Hierarchical Multi-Agent Decision-Making with LLM-Based Agents in Interactive Environments](https://mlsanity.com/paper/2606.03698/) (2026)
- [Using Reward Uncertainty to Induce Diverse Behaviour in Reinforcement Learning](https://mlsanity.com/paper/2606.03962/) (2026)
- [MIRO: MultI-Reward cOnditioned pretraining improves T2I quality and efficiency](https://mlsanity.com/paper/2510.25897/) (2025)
- [Toward Plasticity-Preserving KL Regularization for Capability Retention in LLM Reinforcement Learning](https://mlsanity.com/paper/2608.01743/) (2026)
- [RLVR is a Kernel, Not a Function: Statistical Inference for pass@k Crossovers](https://mlsanity.com/paper/2609.22547/) (2026)
- [Exploration-Driven Optimization for Test-Time Large Language Model Reasoning](https://mlsanity.com/paper/2605.09853/) (2026)
- [ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples](https://mlsanity.com/paper/2607.10481/) (2026)
- [More Is Not More: What Matters for Diversity in LLM Opinions?](https://mlsanity.com/paper/2607.20429/) (2026)
- [Beyond Search-Imitation: Prior-Directed Exploration for Searchless Chess](https://mlsanity.com/paper/2608.27757/) (2026)

## Abstract (arXiv)

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We show -- mathematically and empirically -- that this intuition does not necessarily transfer well to doing reinforcement learning with reverse/forward KL regularization (e.g. as commonly used with language models). Instead, the choice of reverse/forward KL determines the family of optimal target distributions, parameterized by the regularization coefficient. Mode coverage depends primarily on other factors, such as regularization strength, and relative scales between rewards and reference probabilities. Further, we show commonly used settings such as low regularization strength and equal verifiable rewards tend to specify unimodal target distributions, meaning the optimization objective is, by construction, non-diverse. We leverage these insights to construct a simple, scalable, and theoretically justified algorithm. It makes minimal changes to reward magnitudes, yet optimizes for a target distribution which puts high probability over all high-quality sampling modes. In experiments, this simple modification works to post-train both Large Language Models and Chemical Language Models to have higher solution quality and diversity, without any external signals of diversity, and works with both forward and reverse KL when using either naively fails.