Robust Nash Alignment under Preference Uncertainty

Preference-based fine-tuning methods such as RLHF and DPO require substantial compute and large preference datasets. They also need direct access to the model parameters which are not provided by many state-of-the art models. Inference-time alignment offers a cost-effective alternative without updating model parameters. However, existing inference-time methods rely on a scalar reward model derived under a Bradley-Terry assumption, which cannot represent general preferences. Following recent work on fine-tuning with generalized preferences, in this work, we initiate the study of inference-time alignment under general preferences. We formulate the problem as obtaining a Nash equilibrium of a two-player zero-sum game between policies. We propose two algorithms: Best-of-Nash (BoN) and Nash Mirror Descent (NMD). We prove that both algorithms achieve a duality gap that matches the problem lower bound. Empirically, we implement the two methods on three datasets, which shows that our methods substantially outperform the base policy, converging to the performance of the fine-tuned models. Moreover, our results show that NMD remains robust across the regularization parameter.

Existing robust preference optimization for language-model alignment mainly studies pairwise supervision and places robustness at the dataset, prompt, or preference-pair level. We instead study listwise preference optimization under ranking-label uncertainty: given a prompt and a candidate list, the observed ranking over that list may be ambiguous due to annotator inconsistency, near-ties, lossy rankwise feedback, or reward-model noise. We propose a pointwise total-variation robust Plackett--Luce objective that directly robustifies the ranking label conditional on the candidate list. The robust loss admits an exact decomposition into the nominal PL loss plus a worst-case PL correction, and the worst-case ranking is obtained by sorting current implicit scores in ascending order, reducing the inner maximization from $K!$ enumeration to $O(K\log K)$. This tractable structure yields strong offline and online optimization guarantees. In the offline fixed-list setting, the robust objective is convex and projected stochastic subgradient reaches global $ε$-suboptimality with $O(ε^{-2})$ sample complexity. In the online policy-induced setting, where candidate lists are generated by the current policy, we establish weak convexity and $\widetilde O(ε^{-2})$ Moreau-envelope stationarity. Experiments in offline LLM alignment show that the proposed robust correction largely preserves performance under clean labels and improves robustness under noise. In online alignment, it makes reward-model-ranked candidate expansion more reliable and improves both reward-model and external GPT-4 judge metrics.

Aligning large language models (LLMs) to serve users with heterogeneous and potentially conflicting preferences is a central challenge for personalized and trustworthy AI. We formalize an ideal notion of universal alignment through test-time scaling: for each prompt, the model produces $k\ge 1$ candidate responses and a user selects their preferred one. We introduce $(k,f(k))$-robust alignment, which requires the $k$-output model to have win rate $f(k)$ against any other single-output model, and asymptotic universal alignment (U-alignment), which requires $f(k)\to 1$ as $k\to\infty$. Our main result characterizes the optimal convergence rate: there exists a family of single-output policies whose $k$-sample product policies achieve U-alignment at rate $f(k)=\frac{k}{k+1}$, and no method can achieve a faster rate in general. We show that popular post-training methods, including Nash learning from human feedback (NLHF), can fundamentally underutilize the benefits of test-time scaling. Even though NLHF is optimal for $k=1$, sampling from the resulting (often deterministic) policy cannot guarantee win rates above $\tfrac{1}{2}$ except for an arbitrarily small slack. This stems from a lack of output diversity: existing alignment methods can collapse to a single majority-preferred response, making additional samples redundant. In contrast, our approach preserves output diversity and achieves the optimal test-time scaling rate. In particular, we propose a family of symmetric multi-player alignment games and prove that any symmetric Nash equilibrium policy of the $(k+1)$-player alignment game achieves the optimal $(k,\frac{k}{k+1})$-robust alignment. Finally, we provide theoretical convergence guarantees for self-play learning dynamics in these games and extend the framework to opponents that also generate multiple responses.