# Tail-Likelihood Reinforcement Learning

arXiv: https://arxiv.org/abs/2609.02987 · HTML: https://mlsanity.com/paper/2609.02987/

## Key facts

- Cited by 3 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 40 of its 105 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## 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 40)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Defining and Characterizing Reward Hacking](https://mlsanity.com/paper/2209.13085/) (2022)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [RLTF: Reinforcement Learning from Unit Test Feedback](https://mlsanity.com/paper/2307.04349/) (2023)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Execution-based Code Generation using Deep Reinforcement Learning](https://mlsanity.com/paper/2301.13816/) (2023)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [ACECODER: Acing Coder RL via Automated Test-Case Synthesis](https://mlsanity.com/paper/2502.01718/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Kevin: Multi-Turn RL for Generating CUDA Kernels](https://mlsanity.com/paper/2507.11948/) (2025)
- [StepCoder: Improve Code Generation with Reinforcement Learning from Compiler Feedback](https://mlsanity.com/paper/2402.01391/) (2024)
- [Optimizing Language Models for Inference Time Objectives using Reinforcement Learning](https://mlsanity.com/paper/2503.19595/) (2025)
- [Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration](https://mlsanity.com/paper/2508.13755/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives](https://mlsanity.com/paper/2510.04996/) (2025)
- [Differential Smoothing Mitigates Sharpening and Improves LLM Reasoning](https://mlsanity.com/paper/2511.19942/) (2025)

## Built on by (most cited first, 3 of 3)

- [Matryoshka attribution: Learning to attribute language model outputs to representations and weights](https://mlsanity.com/paper/2609.25518/) (2026)
- [EasyPPO: Stabilizing the Critic Is Key](https://mlsanity.com/paper/2609.36802/) (2026)
- [Balancing Reference Guidance and Free Generation in Trajectory Rollouts for Reasoning RL](https://mlsanity.com/paper/2610.11128/) (2026)

## Abstract (arXiv)

Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-k gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.