# SquarechiPO: Differentially Private and Robust chi2-Preference Optimization in Offline Direct Alignment

arXiv: https://arxiv.org/abs/2505.21395 · HTML: https://mlsanity.com/paper/2505.21395/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Human values and AI feedback alignment, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 70 of its 96 references that are in the map.
- First posted on arXiv 27 May 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Human values and AI feedback alignment](https://mlsanity.com/alignment/human-values-and-ai-feedback-alignment/)

## Builds on (most cited first, 30 of 70)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (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)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Principle-Driven Self-Alignment of Language Models from Scratch with Minimal Human Supervision](https://mlsanity.com/paper/2305.03047/) (2023)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Generalized Preference Optimization: A Unified Approach to Offline Alignment](https://mlsanity.com/paper/2402.05749/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)

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

- [Improved Bounds for Private and Robust Alignment](https://mlsanity.com/paper/2512.23816/) (2025)
- [Reinforcement Learning from Human Feedback: A Statistical Perspective](https://mlsanity.com/paper/2604.02507/) (2026)
- [Privacy Without Regret: Differentially Private Inference-Time Alignment](https://mlsanity.com/paper/2608.26324/) (2026)

## Abstract (arXiv)

In this paper, we theoretically study the offline alignment of language models with human preference feedback, under both preference label corruption and privacy protections. To this end, we propose SquarechiPO, a simple one-line change to chiPO where the standard log-loss is replaced by a new square loss over probability. Thanks to the inherent properties of this new loss, we have advanced the state-of-the-art of differentially private and robust offline direct alignment. Specifically, for the local model of label privacy, SquarechiPO is the first algorithm that attains an optimal rate based on single-policy concentrability even with general function approximations. It also gives the first result under the central model of privacy protection over both prompts (responses) and labels. On the robustness side against Huber label corruption, SquarechiPO is the first alignment method that has a meaningful theoretical guarantee under general function approximations. More importantly, SquarechiPO can address privacy protection and corruption simultaneously, where an interesting separation is observed, implying that the order of privacy and corruption matters. Furthermore, we show that SquarechiPO can also be easily extended to handle the scenario of the general preference model with state-of-the-art guarantees under corruption and privacy. Last but not least, all of our theoretical guarantees enjoy a unified analysis, building upon a new result on the generalization error bounds of least-square regression under corruption and privacy constraints, which we believe is of independent interest to the community.