# Reward Shaping for (Inference-Time) Alignment: A Stackelberg Game Perspective

arXiv: https://arxiv.org/abs/2602.02572 · HTML: https://mlsanity.com/paper/2602.02572/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 49 of its 61 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 49)

- [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)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Persistent Anti-Muslim Bias in Large Language Models](https://mlsanity.com/paper/2101.05783/) (2021)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [A Contrastive Framework for Neural Text Generation](https://mlsanity.com/paper/2202.06417/) (2022)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Red-Teaming Large Language Models using Chain of Utterances for Safety-Alignment](https://mlsanity.com/paper/2308.09662/) (2023)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Gender bias and stereotypes in Large Language Models](https://mlsanity.com/paper/2308.14921/) (2023)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Controlled Decoding from Language Models](https://mlsanity.com/paper/2310.17022/) (2023)
- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Verbosity Bias in Preference Labeling by Large Language Models](https://mlsanity.com/paper/2310.10076/) (2023)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [Aligning Large Language Models with Representation Editing: A Control Perspective](https://mlsanity.com/paper/2406.05954/) (2024)
- [Incomplete Contracting and AI Alignment](https://mlsanity.com/paper/1804.04268/) (2018)
- [DeAL: Decoding-time Alignment for Large Language Models](https://mlsanity.com/paper/2402.06147/) (2024)
- [CULTURE-GEN: Revealing Global Cultural Perception in Language Models through Natural Language Prompting](https://mlsanity.com/paper/2404.10199/) (2024)
- [GenARM: Reward Guided Generation with Autoregressive Reward Model for Test-time Alignment](https://mlsanity.com/paper/2410.08193/) (2024)

## Built on by (most cited first, 2 of 2)

- [Reward Hacking in the Era of Large Models: Mechanisms, Emergent Misalignment, Challenges](https://mlsanity.com/paper/2604.13602/) (2026)
- [Explaining and Preventing Alignment Collapse in Iterative RLHF](https://mlsanity.com/paper/2605.04266/) (2026)

## Abstract (arXiv)

Existing alignment methods directly use the reward model learned from user preference data to optimize an LLM policy, subject to KL regularization with respect to the base policy. This practice is suboptimal for maximizing user's utility because the KL regularization may cause the LLM to inherit the bias in the base policy that conflicts with user preferences. While amplifying rewards for preferred outputs can mitigate this bias, it also increases the risk of reward hacking. This tradeoff motivates the problem of optimally designing reward models under KL regularization. We formalize this reward model optimization problem as a Stackelberg game, and show that a simple reward shaping scheme can effectively approximate the optimal reward model. We empirically evaluate our method in inference-time alignment settings and demonstrate that it integrates seamlessly into existing alignment methods with minimal overhead. Our method consistently improves average reward and achieves win-tie rates exceeding 66% against all baselines, averaged across evaluation settings.