We study learning a mixture of k Plackett-Luce models from multi-way ranking responses from annotators that may represent heterogeneous underlying preferences. This problem has many applications in AI alignment and preference optimization. Prior work has studied mixtures of Bradley-Terry models from pairwise comparisons. However, estimating a mixture of multi-way ranking models can become theoretically unidentifiable when k exceeds m/2, where m is the ranking length. We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size (e.g., generating comparisons from a base model), followed by a gradient-based estimation to reduce inference cost (in the input embedding space). With this procedure in mind, we then fit a mixture of Plackett-Luce (PL) models via an expectation-maximization-style iteration, or MoPLEx in short. We conduct extensive experiments to verify this algorithm. First, we find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters. Second, MoPLEx improves clustering and ranking accuracy by an average of 43.7% and 15.2% over baselines using a single PL model or a mixture of Bradley-Terry models, on UltraFeedback and PERSONA datasets. These results demonstrate the effectiveness of MoPLEx for tackling multi-way rankings following heterogeneous preferences through measuring alignment via gradients.
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(KlogK). 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 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.
People hold diverse, sometimes conflicting values, so no single aligned model can satisfy everyone. Pluralistic alignment therefore calls for steerable models that can balance competing objectives differently. Multi-Objective Direct Preference Optimization (MODPO) does this by using an objective weight to span a continuum of trade-offs. We study two questions: when can one model improve two objectives simultaneously, and how can many trade-offs be covered without training a separate model for each? Across seven objective pairs from HelpSteer and UltraFeedback, two pre-training measurements predict whether objectives align or conflict for human-annotated data, but not for AI-annotated data, where response length and repetition confound reward-model scores. For broader trade-off coverage, selecting the nearest trained model and merging model parameters both help, but neither consistently matches direct training. These findings yield practical guidance for building steerable models that serve diverse preferences.
Pairwise preference data is widely used in language-model evaluation and alignment, often for model ranking, reward modeling, or preference optimization. This note formulates a more basic measurement question: given a reference distribution of pairwise preferences, what model-level quantity is estimated when we test whether a model ranks preferred responses above rejected responses? We define pairwise reference alignment as an ordinal observable induced by a model scoring function. Given a reference pair distribution Ppair over triples (x,y+,y−), and a scalar model score SM(x,y), we define the alignment observable as the probability that the model-induced ordering agrees with the reference preference ordering. We further define a centered order-parameter-like statistic and discuss a margin-based extension. The resulting quantities admit simple finite-sample estimators and concentration bounds under independent sampling assumptions. This note does not introduce a new benchmark. It provides a conceptual and statistical formulation for pairwise reference alignment, clarifies the role of the reference pair distribution, and distinguishes the general ordinal observable from scoring choices such as normalized log-probability or energy-based scores. We also provide an initial empirical study on Qwen2.5 models and RewardBench, where the proposed statistics increase with model size and instruction tuning and vary across reference-pair subsets as predicted by the formulation.