MINT: Min-Selection Preference Distillation for Balanced Multi-Objective Alignment
Organizations: Georgia Institute of Technology · Zillow Group
Abstract
Aligning a language agent to several objectives at once is a persistent failure mode of preference-based training: when objectives are combined additively, optimization collapses onto whichever is cheapest to improve and sacrifices the rest, so a support agent learns to sound warm while giving no real help. The root issue is that an additive reward has no notion of balance. We introduce Mint (MIN-selection preference disTillation), a one-line change to preference distillation: rather than ranking sampled candidates by a weighted sum of rewards, we rank them by their weakest objective, distilling the best-balanced candidate over the most lopsided one with an unchanged DPO objective. This is the p -> negative infinity limit of a generalized-mean family spanning additive to worst-case selection. Across cooperative emotional support and adversarial negotiation, min-selection lifts both objectives while sharply cutting their imbalance; on emotional support it raises the weaker axis from 0.37 to 0.64 (p < 10^-40), surpassing human experts and persisting across full multi-turn rollouts. A turn-by-turn analysis yields our central finding: min-selection corrects imbalance in proportion to how imbalanced the reference policy is, and its benefit endures over an interaction precisely as long as that imbalance does.
Figures & tables
| Reference | Mint | Mint Ref | |||||||||
| Depth | AQ | EQ | min ‡ | AQ | EQ | min ‡ | AQ | EQ | min | ||
| ESConv (emotional support): Mint vs. SFT reference – advantage persists across depth | |||||||||||
| 1 | 0.356 | 0.623 | 0.380 | 0.300 | 0.535 | 0.777 | 0.242 | 0.535 | +0.179 | +0.154 | +0.235 |
| 2 | 0.472 | 0.644 | 0.287 | 0.415 | 0.643 | 0.788 | 0.171 | 0.630 | +0.171 | +0.144 | +0.215 |
| 3 | 0.519 | 0.568 | 0.282 | 0.403 | 0.695 | 0.772 | 0.158 | 0.655 | +0.176 | +0.204 | +0.252 |
| 4 | 0.498 | 0.485 | 0.299 | 0.342 | 0.708 | 0.692 | 0.207 | 0.596 | +0.210 | +0.207 | +0.254 |
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
| Criterion | Description | |
| AQ , Action / Helpfulness Quality (substance and specificity) | ||
| Provides Concrete Help | 0.35 | Specificity of help: vague gesture ; generic suggestion – ; specific substantive suggestion or concrete fact – . |
| Offers a Usable Next Step | 0.30 | Vague direction ; simple step ; clear step tailored to the situation . |
| Relevance to the Situation | 0.35 | Generic ; relevant to the general problem ; addresses specific circumstances . |
| EQ , Emotional / Comfort Quality (validation, warmth, timing) | ||
| Validates Emotions | 0.40 | Acknowledges or normalises feelings; naming/reflecting the feeling scores moderate-to-high even if brief. |
| Criterion | Description | |
| AQ , Deal Advantage (price/economic substance only) | ||
| Holds or Improves Price | 0.45 | Caving to a low buyer price ; holding firm near target ; extracting a higher price . A friendly tone does not raise this score. |
| Justifies with Value | 0.25 | Concrete reason the price is warranted (condition, features, demand). Bare “no” ; specific value argument . |
| Advances to Close | 0.30 | Concrete step toward finalising (counter-offer, terms). Stalling ; clear actionable proposal . |
| EQ , Interpersonal Warmth (tone/language only) | ||
| Warmth of Language | 0.45 | Curt/robotic (“7, deal.”) – even if it closes a good deal ; warm, personable phrasing even if the price is bad . |
Multi-Objective Language Model Alignment
Multi-objective language model alignment studies how to balance competing goals such as helpfulness, safety, truthfulness, fairness, and personalization.
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