Relation-Aware Preference Optimization

• Relation-aware preference optimization is a framework that incorporates structural, semantic, and ordinal relations to enrich preference signals in learning systems.
• It employs methods like listwise alignment, semantic similarity weighting, and token-level ambiguity detection to refine output in tasks such as LLM alignment and KGQA.
• Empirical results demonstrate gains of 3–4 percentage points in ranking metrics and improved win rates, evidencing its practical impact across diverse applications.

Relation-aware preference optimization refers to a class of optimization strategies that leverage explicit inter- or intra-sample relations—structural, semantic, or ordinal—in the formation and exploitation of preference signals within learning systems. This paradigm generalizes traditional pairwise preference optimization by making use of higher-order structures, semantic proximities, or intermediate reasoning steps, with applications spanning from relational database queries to reinforcement learning from human feedback (RLHF) in LLMs and knowledge-intensive tasks such as knowledge graph question answering (KGQA).

1. Foundational Principles

The central objective of relation-aware preference optimization is to move beyond isolated, atomized preference signals (such as simple pairwise “win/loss”) and instead harness broader context: relationships among multiple items, semantic or structural proximity in input space, or intermediate reasoning chains. The approach has its origins in early database work on semantic optimization of preference queries, where integrity constraints (functional dependencies, inclusion dependencies) are exploited to streamline candidate comparisons and eliminate redundant preference computation [0402003]. More recently, the concept has been extended to LLM alignment (as in OPO, RPO, AAO) and KGQA with knowledge-grounded reasoning (Zhao et al., 2024, Yin et al., 2024, Li et al., 28 Nov 2025, Um et al., 27 Jan 2026).

At a high level, relation-aware methods introduce one or more of the following relation-driven mechanisms:

• Listwise alignment: Using full or partial orderings over sets, not just binary preferences.
• Semantic similarity weighting: Adjusting learning signals according to the proximity of examples in some embedding or graph space.
• Step-wise reasoning supervision: Exploiting intermediate relational or logical structures to refine multi-step optimization.

2. Methodologies in Relation-Aware Preference Optimization

Several algorithmic instantiations exist, each exploiting relations in distinct ways:

Approach	Type of Relation Injected	Typical Loss/Optimization	Reference
OPO	Ordinal/Ranking (listwise among K)	NeuralNDCG surrogate loss	(Zhao et al., 2024)
RPO	Cross-prompt semantic proximity	Contrastive, weighted pairwise	(Yin et al., 2024)
AAO	Token-level semantic similarity within pair	Weighted DPO at token level	(Li et al., 28 Nov 2025)
RPO-RAG	Semantic clustering of reasoning paths in KG	Margin-based, per-relation preference	(Um et al., 27 Jan 2026)

Listwise methods (e.g., OPO) optimize over permutations or ranked lists, using metrics such as NDCG, as opposed to pairwise cross-entropy. Contrastive methods (RPO) introduce similarity-based weighting between responses to both identical and related prompts, filling a contrastive matrix over all possible win–lose pairs in a batch. Ambiguity-aware methods (AAO) operate on token alignments within preference pairs, down-weighting ambiguous, semantically redundant tokens to resolve canceling gradients at the sequence level.

In KGQA (RPO-RAG), the relation-aware module provides supervision at each step of a KG path reasoning chain, clustering sampled paths to determine sets of preferred and non-preferred relations per step, and weighting model updates accordingly (Um et al., 27 Jan 2026).

3. Mathematical Formulations

The relation-aware framework is unified by the introduction of weights or loss modifications based on explicit or implicit relations:

• Listwise NDCG optimization (OPO): Given $K$ responses per prompt with labels $\psi_1 \geq \dots \geq \psi_K$ and model scores $s_1, \dots, s_K$, the normalized discounted cumulative gain (NDCG) is approximated via a differentiable surrogate using soft permutations and Sinkhorn scaling:

$$\mathrm{NeuralNDCG}@K = \frac{1}{\mathrm{IDCG}@K} \sum_{i=1}^K \bigl[\mathrm{Sinkhorn}(\widehat{P})\,G(\mathbf{\Psi})\bigr]_i D(i)$$

where $G(\psi)$ and $D(i)$ are gain and discount functions (Zhao et al., 2024).

• Relative preference contrastive weighting (RPO):

$$L_\mathrm{RPO} = -\frac{1}{MN} \sum_{i=1}^M \sum_{j=1}^N \log \sigma( \omega_{ij}\, \Delta r_{ij} )$$

with $\omega_{ij}$ the normalized semantic proximity weight between prompts, and $\Delta r_{ij}$ the difference in model log-odds between win and lose responses (Yin et al., 2024).

• Ambiguity-aware token reweighting (AAO):

$$\log \pi_\theta^\mathrm{w\,AAO}(y_w|x) = \sum_{i} w_w^{(i)} \log P_\theta(y_w^{(i)}|...)$$

where $w_w^{(i)}$ is adaptively determined via token-level semantic similarity, using piecewise or smoothed sigmoidal functions (Li et al., 28 Nov 2025).

• Relation-aware KG reasoning (RPO-RAG):

$$\mathcal{L}_\mathrm{relpref}(\theta) = -\mathbb{E}_{(x,y^+,y^-)}\Bigl[\log\sigma( W^+\,\log\pi_\theta(y^+|x) - W^-\,\log\pi_\theta(y^-|x) - \gamma)\Bigr]$$

where $W^\pm$ are mean confidence weights over preferred/non-preferred relations induced by semantic clustering of reasoning paths (Um et al., 27 Jan 2026).

4. Implementation and Empirical Validation

The implementation of relation-aware preference optimization varies by application domain.

In LLM alignment, OPO and RPO are integrated into fine-tuning workflows post-supervised learning, reweighting preference objective gradients according to relation-aware signals. OPO leverages NeuralNDCG to approximate non-differentiable ranking losses; RPO builds batch-level contrast matrices using frozen embedding encoders (e.g., all-MiniLM-L6-v2) to compute semantic similarities. AAO’s ambiguity detection exploits localized embeddings from internal model layers, learning adaptive thresholds for semantic similarity.

In KG-based RAG (RPO-RAG), shortest reasoning paths connecting question and answer entities are enumerated and clustered; relation-aware optimization then supervises the LLM at every hop through adaptive confidence weights, with SGD updates governed by margin-based losses. Hyperparameter tuning of decay rates, margins, and loss scales is essential to maximize performance under various model budgets (Um et al., 27 Jan 2026).

Empirical results consistently demonstrate that relation-aware strategies yield substantial improvements over baseline pairwise approaches. For instance, OPO achieves gains up to 3–4 percentage points on AlpacaEval (small models) and 87.5% win rate (Mistral-7B) versus 83–86% for other leading baselines (Zhao et al., 2024). RPO boosts win rates on the Anthropic Helpful–Harmless dataset from 72.3% (DPO) to 78.5% (paired, τ=0.5) (Yin et al., 2024). In KGQA, RPO-RAG’s relation-aware module delivers an 8.8-point F1 improvement on WebQSP and 6–8 point Hit and 10–13 point F1 gains are lost when it is removed (Um et al., 27 Jan 2026). AAO demonstrates raw win rate improvements on AlpacaEval 2 (31.3% to 40.2%) and Arena-Hard (26.0% to 41.0%) for Llama 3.1-8B (Li et al., 28 Nov 2025).

5. Comparative Analysis and Advantages

Relation-aware preference optimization provides several intrinsic benefits:

• Efficient Gradient Propagation: Listwise and token-aware approaches diffuse gradients over entire sets or sequences, reducing sparse signaling and better exploiting the available preference information (OPO, AAO).
• Robustness to Ambiguity and Noisy Supervision: Semantic weighting mitigates the effects of highly ambiguous, copied, or redundant content, focusing learning signals on distinctive features (AAO, RPO).
• Enhanced Generalization: By considering contrast pairs across related but non-identical contexts, RPO better models human-like preference learning, leading to improved adaptability in open-ended tasks.
• Interpretability in Multi-hop Reasoning: In KGQA, relation-aware losses make the model’s multistep reasoning process traceable and align intermediate decisions with intended semantics (RPO-RAG), a feature not present in black-box pairwise optimization.

Relation-aware methods typically reduce to their pairwise or sequence-level counterparts when relation-induced weights are uniform or off-diagonal matrix entries are suppressed, confirming the generality of the framework.

6. Limitations and Research Directions

Known limitations pertain to scalability (as full M×N contrast matrices grow rapidly with batch size in RPO), dependence on ancillary models (e.g., embedding encoders in RPO), and the challenge of learning truly optimal reweighting schemes as datasets and preference spaces become more complex (Yin et al., 2024, Li et al., 28 Nov 2025). Additionally, listwise objectives such as OPO require differentiable approximations to ranking metrics, which may imperfectly reflect the true discrete optimization objective (Zhao et al., 2024).

Open research questions include:

• Automatic inference and learning of optimal weighting and token similarity curves (as opposed to hand-designed piecewise/sigmoid functions).
• Extension to multi-branch or continuous preference structures (e.g., multiple objectives, smooth preference dispersions).
• Joint, end-to-end learning of relation structures and policy parameters, especially when off-the-shelf encoders for semantic similarity are suboptimal or mismatched to the downstream domain.
• Exploiting sparse or transport-based batches for efficient computation in high-cardinality relation matrices.
• Cross-domain transfer and adaptation of relation-aware techniques developed in LLM alignment to relational databases or graph-structured tasks, or vice versa.

7. Broader Impact and Outlook

Relation-aware preference optimization represents a foundational advance in the alignment and efficiency of modern machine learning systems. By incorporating the structure and semantics of inter-item, intra-sequence, or graph-based relations directly into the optimization objective, these methods deliver significant improvements in performance, interpretability, and adaptability across language modeling, database query optimization, and knowledge-intensive reasoning [0402003, (Zhao et al., 2024, Yin et al., 2024, Li et al., 28 Nov 2025, Um et al., 27 Jan 2026)].

This approach is likely to remain central in ongoing research into controllable alignment, efficient KG reasoning, and the development of compact models capable of high-quality, human-consistent behavior in complex preference and decision environments.