# Decoding-Time Language Model Alignment with Multiple Objectives

arXiv: https://arxiv.org/abs/2406.18853 · HTML: https://mlsanity.com/paper/2406.18853/

## Key facts

- Cited by 94 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 50 of its 67 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [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)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Personalized Soups: Personalized Large Language Model Alignment via Post-hoc Parameter Merging](https://mlsanity.com/paper/2310.11564/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [WARM: On the Benefits of Weight Averaged Reward Models](https://mlsanity.com/paper/2401.12187/) (2024)
- [HelpSteer: Multi-attribute Helpfulness Dataset for SteerLM](https://mlsanity.com/paper/2311.09528/) (2023)
- [Controlled Decoding from Language Models](https://mlsanity.com/paper/2310.17022/) (2023)
- [Calibrating Sequence likelihood Improves Conditional Language Generation](https://mlsanity.com/paper/2210.00045/) (2022)

## Built on by (most cited first, 30 of 94)

- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [A Survey of Personalized Large Language Models: Progress and Future Directions](https://mlsanity.com/paper/2502.11528/) (2025)
- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [PAD: Personalized Alignment of LLMs at Decoding-Time](https://mlsanity.com/paper/2410.04070/) (2024)
- [GenARM: Reward Guided Generation with Autoregressive Reward Model for Test-time Alignment](https://mlsanity.com/paper/2410.08193/) (2024)
- [Multi-Attribute Steering of Language Models via Targeted Intervention](https://mlsanity.com/paper/2502.12446/) (2025)
- [Conditional Language Policy: A General Framework for Steerable Multi-Objective Finetuning](https://mlsanity.com/paper/2407.15762/) (2024)
- [A Survey on Personalized Alignment -- The Missing Piece for Large Language Models in Real-World Applications](https://mlsanity.com/paper/2503.17003/) (2025)
- [LoRe: Personalizing LLMs via Low-Rank Reward Modeling](https://mlsanity.com/paper/2504.14439/) (2025)
- [Personality Alignment of Large Language Models](https://mlsanity.com/paper/2408.11779/) (2024)
- [Controllable Safety Alignment: Inference-Time Adaptation to Diverse Safety Requirements](https://mlsanity.com/paper/2410.08968/) (2024)
- [When One LLM Drools, Multi-LLM Collaboration Rules](https://mlsanity.com/paper/2502.04506/) (2025)
- [PARM: Multi-Objective Test-Time Alignment via Preference-Aware Autoregressive Reward Model](https://mlsanity.com/paper/2505.06274/) (2025)
- [The Crucial Role of Samplers in Online Direct Preference Optimization](https://mlsanity.com/paper/2409.19605/) (2024)
- [A Survey on Personalized and Pluralistic Preference Alignment in Large Language Models](https://mlsanity.com/paper/2504.07070/) (2025)
- [ALFA: Aligning LLMs to Ask Good Questions A Case Study in Clinical Reasoning](https://mlsanity.com/paper/2502.14860/) (2025)
- [Weak-to-Strong Preference Optimization: Stealing Reward from Weak Aligned Model](https://mlsanity.com/paper/2410.18640/) (2024)
- [Robust Multi-Objective Preference Alignment with Online DPO](https://mlsanity.com/paper/2503.00295/) (2025)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Self-Improvement Towards Pareto Optimality: Mitigating Preference Conflicts in Multi-Objective Alignment](https://mlsanity.com/paper/2502.14354/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [On Almost Surely Safe Alignment of Large Language Models at Inference-Time](https://mlsanity.com/paper/2502.01208/) (2025)
- [Bone Soups: A Seek-and-Soup Model Merging Approach for Controllable Multi-Objective Generation](https://mlsanity.com/paper/2502.10762/) (2025)
- [Drift: Decoding-time Personalized Alignments with Implicit User Preferences](https://mlsanity.com/paper/2502.14289/) (2025)
- [Multi-Objective Preference Optimization: Improving Human Alignment of Generative Models](https://mlsanity.com/paper/2505.10892/) (2025)
- [Multi-objective Large Language Model Alignment with Hierarchical Experts](https://mlsanity.com/paper/2505.20925/) (2025)
- [CoSteer: Collaborative Decoding-Time Personalization via Local Delta Steering](https://mlsanity.com/paper/2507.04756/) (2025)
- [Fast Large Language Model Collaborative Decoding via Speculation](https://mlsanity.com/paper/2502.01662/) (2025)
- [Robustness in Large Language Models: A Survey of Mitigation Strategies and Evaluation Metrics](https://mlsanity.com/paper/2505.18658/) (2025)

## Abstract (arXiv)

Aligning language models (LMs) to human preferences has emerged as a critical pursuit, enabling these models to better serve diverse user needs. Existing methods primarily focus on optimizing LMs for a single reward function, limiting their adaptability to varied objectives. Here, we propose multi-objective decoding (MOD), a decoding-time algorithm that outputs the next token from a linear combination of predictions of all base models, for any given weightings over different objectives. We exploit a common form among a family of f-divergence regularized alignment approaches (such as PPO, DPO, and their variants) to identify a closed-form solution by Legendre transform, and derive an efficient decoding strategy. Theoretically, we show why existing approaches can be sub-optimal even in natural settings and obtain optimality guarantees for our method. Empirical results demonstrate the effectiveness of the algorithm. For example, compared to a parameter-merging baseline, MOD achieves 12.8% overall reward improvement when equally optimizing towards 3 objectives. Moreover, we experiment with MOD on combining three fully-finetuned LLMs of different model sizes, each aimed at different objectives such as safety, coding, and general user preference. Unlike traditional methods that require careful curation of a mixture of datasets to achieve comprehensive improvement, we can quickly experiment with preference weightings using MOD to find the best combination of models. Our best combination reduces toxicity on Toxigen to nearly 0% and achieves 7.9--33.3% improvement across other three metrics (textiti.e., Codex@1, GSM-COT, BBH-COT).