Theoretical Bounds for Private and Robust Language Model Alignment

A new theoretical study from arXiv examines how to align language models when training data must satisfy privacy requirements and resistance to adversarial attacks. The research establishes upper bounds on the suboptimality gap—the performance shortfall compared to an ideal scenario—in both offline and online settings.

Key Findings#

The work analyzes preference labels that are subject to privacy constraints, adversarial corruption, or both. The researchers explore two distinct scenarios:

• Privacy-first: Where privacy concerns take precedence
• Corruption-first: Where robustness to adversarial attacks takes precedence

For alignment with privacy alone, the authors show that log loss combined with an MLE-style (maximum likelihood estimation) algorithm achieves near-optimal rates. This challenges conventional assumptions about how privacy fundamentally hampers learning efficiency.

Stronger Guarantees in Combined Settings#

When both privacy and corruption must be handled together, the team demonstrates that existing offline algorithms actually provide stronger guarantees than previously recognized. These improvements apply simultaneously to both corruption tolerance and privacy parameters, and even yield better bounds in corruption-only scenarios.

Online Alignment Results#

The paper also presents the first theoretical results for private and robust online alignment, extending the guarantees to dynamic settings where data arrives sequentially.

The researchers develop new uniform convergence guarantees for log loss and square loss under both privacy and corruption constraints, which they suggest have broader applications across learning theory and statistics.