# Learning to Reason Efficiently with Discounted Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.23486 · HTML: https://mlsanity.com/paper/2510.23486/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 57 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 27 of 27)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [How Well do LLMs Compress Their Own Chain-of-Thought? A Token Complexity Approach](https://mlsanity.com/paper/2503.01141/) (2025)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [Sample More to Think Less: Group Filtered Policy Optimization for Concise Reasoning](https://mlsanity.com/paper/2508.09726/) (2025)
- [Effectively Controlling Reasoning Models through Thinking Intervention](https://mlsanity.com/paper/2503.24370/) (2025)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Just Enough Thinking: Efficient Reasoning with Adaptive Length Penalties Reinforcement Learning](https://mlsanity.com/paper/2506.05256/) (2025)
- [Prolonged Reasoning Is Not All You Need: Certainty-Based Adaptive Routing for Efficient LLM/MLLM Reasoning](https://mlsanity.com/paper/2505.15154/) (2025)
- [ConCISE: Confidence-guided Compression in Step-by-step Efficient Reasoning](https://mlsanity.com/paper/2505.04881/) (2025)
- [Thinking Fast and Right: Balancing Accuracy and Reasoning Length with Adaptive Rewards](https://mlsanity.com/paper/2505.18298/) (2025)
- [Train Long, Think Short: Curriculum Learning for Efficient Reasoning](https://mlsanity.com/paper/2508.08940/) (2025)
- [Fast on the Easy, Deep on the Hard: Efficient Reasoning via Powered Length Penalty](https://mlsanity.com/paper/2506.10446/) (2025)
- [ConciseRL: Conciseness-Guided Reinforcement Learning for Efficient Reasoning Models](https://mlsanity.com/paper/2505.17250/) (2025)
- [SABER: Switchable and Balanced Training for Efficient LLM Reasoning](https://mlsanity.com/paper/2508.10026/) (2025)
- [Scaling Up RL: Unlocking Diverse Reasoning in LLMs via Prolonged Training](https://mlsanity.com/paper/2507.12507/) (2025)

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

- [Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents](https://mlsanity.com/paper/2604.05164/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Learning When to Think: Adaptive Reasoning for Test-Time Compute Allocation](https://mlsanity.com/paper/2608.20256/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) often consume excessive tokens, inflating computational cost and latency. More broadly, in goal reaching sequential decision problems we often want to reach the goal quickly, and LRM reasoning can be viewed through this lens. We challenge the assumption that longer responses improve accuracy. By penalizing reasoning tokens using a discounted reinforcement learning setup (interpretable as a small token cost) and analyzing Blackwell optimality in restricted policy classes, we encourage concise yet accurate reasoning, analogous to preferring shorter successful trajectories in a stochastic shortest path problem. Experiments confirm our theoretical results that this approach shortens chains of thought while preserving accuracy.