# Improved Bounds for Private and Robust Alignment

arXiv: https://arxiv.org/abs/2512.23816 · HTML: https://mlsanity.com/paper/2512.23816/

## Key facts

- Cited by 5 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 48 of its 61 references that are in the map.
- First posted on arXiv 29 Dec 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 48)

- [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)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [FLAMBE: Structural Complexity and Representation Learning of Low Rank MDPs](https://mlsanity.com/paper/2006.10814/) (2020)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer](https://mlsanity.com/paper/2405.16436/) (2024)
- [Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF](https://mlsanity.com/paper/2405.21046/) (2024)
- [The Role of Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2210.04157/) (2022)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2205.11140/) (2022)
- [Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization](https://mlsanity.com/paper/2407.13399/) (2024)
- [Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning](https://mlsanity.com/paper/2407.15007/) (2024)
- [Value-Incentivized Preference Optimization: A Unified Approach to Online and Offline RLHF](https://mlsanity.com/paper/2405.19320/) (2024)
- [Preference-based Reinforcement Learning with Finite-Time Guarantees](https://mlsanity.com/paper/2006.08910/) (2020)
- [Provable Offline Preference-Based Reinforcement Learning](https://mlsanity.com/paper/2305.14816/) (2023)
- [Cautiously Optimistic Policy Optimization and Exploration with Linear Function Approximation](https://mlsanity.com/paper/2103.12923/) (2021)
- [Private Reinforcement Learning with PAC and Regret Guarantees](https://mlsanity.com/paper/2009.09052/) (2020)
- [The History and Risks of Reinforcement Learning and Human Feedback](https://mlsanity.com/paper/2310.13595/) (2023)
- [An Optimal Private Stochastic-MAB Algorithm Based on an Optimal Private Stopping Rule](https://mlsanity.com/paper/1905.09383/) (2019)
- [Multi-Armed Bandits with Local Differential Privacy](https://mlsanity.com/paper/2007.03121/) (2020)
- [Foundations of Reinforcement Learning and Interactive Decision Making](https://mlsanity.com/paper/2312.16730/) (2023)
- [Sharp Analysis for KL-Regularized Contextual Bandits and RLHF](https://mlsanity.com/paper/2411.04625/) (2024)
- [Manipulation Attacks in Local Differential Privacy](https://mlsanity.com/paper/1909.09630/) (2019)
- [When Privacy Meets Partial Information: A Refined Analysis of Differentially Private Bandits](https://mlsanity.com/paper/2209.02570/) (2022)

## Built on by (most cited first, 5 of 5)

- [Near-Optimal Regret for KL-Regularized Multi-Armed Bandits](https://mlsanity.com/paper/2603.02155/) (2026)
- [On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization](https://mlsanity.com/paper/2605.02141/) (2026)
- [Private Direct Preference Optimization for LLM Alignment](https://mlsanity.com/paper/2608.05040/) (2026)
- [WorldMark: A Plug-and-Play World Knowledge Interface for Cross-Host Language Model Watermarking](https://mlsanity.com/paper/2608.06416/) (2026)
- [Overtaught, Underlearned: Learner-Centered Distillation from Multi-Agent Discussion](https://mlsanity.com/paper/2610.16543/) (2026)

## Abstract (arXiv)

In this paper, we study the private and robust alignment of language models from a theoretical perspective by establishing upper bounds on the suboptimality gap in both offline and online settings. We consider preference labels subject to privacy constraints and/or adversarial corruption, and analyze two distinct interplays between them: privacy-first and corruption-first. For the privacy-only setting, we show that log loss with an MLE-style algorithm achieves near-optimal rates, in contrast to conventional wisdom. For the joint privacy-and-corruption setting, we first demonstrate that existing offline algorithms in fact provide stronger guarantees -- simultaneously in terms of corruption level and privacy parameters -- than previously known, which further yields improved bounds in the corruption-only regime. In addition, we also present the first set of results for private and robust online alignment. Our results are enabled by new uniform convergence guarantees for log loss and square loss under privacy and corruption, which we believe have broad applicability across learning theory and statistics.