Cross-Domain Reward Modeling

• Cross-domain reward models are mathematical frameworks that transfer reward signals across diverse environments to enhance generalization and preference modeling.
• They integrate Bayesian estimation, domain-adversarial learning, and modular architectures to balance domain-specific nuances with invariant features.
• Empirical studies show significant gains in robotics, recommender systems, and multimodal tasks, underscoring the approach’s practical and scalable impact.

A cross-domain reward model is a mathematical and algorithmic framework designed to define, infer, or transfer reward signals across multiple distinct operational environments or domains. The principal motivation is to promote generalization, transferability, and robust preference modeling when learning agents, policies, or generative models must operate in heterogeneous or evolving contexts—such as robot control across different physical scenarios, LLM alignment across styles or languages, or recommender systems across diverse user/ad cohorts. The following sections delineate the historical origins, core probabilistic formulations, state-of-the-art architectures, domain adaptation methodologies, empirical validations, and open questions in cross-domain reward modeling.

1. Historical Foundations and Formulations

Early efforts in cross-domain reward modeling arose from the practical need to efficiently design reward functions that guide agent behavior across multiple environments. In conventional robot planning or RL workflows, crafting a reward that generalizes is challenging and iterative; proxy rewards tuned in isolated environments may not transfer directly to new configurations. The divide-and-conquer approach introduced by Ratner et al. (Ratner et al., 2018) formalizes the proxy reward design process: for $N$ environments, the designer independently selects proxy weights $r_i \in \mathbb{R}^k$, which induce desired behavior in environment $M_i$. These are treated as “noisy observations” of an underlying, true reward vector $w \in \mathbb{R}^k$, parameterizing a linear model $R(\xi;w) = w^\top\phi(\xi)$ over feature counts.

The inference of a shared reward involves Bayesian estimation given the proxy set $\{r_i\}$:

$$p(w\,|\,\{r_i\}) \propto p(w) \prod_{i=1}^N p(r_i\,|\,w)$$

where $$p(r_i\,|\,w)\propto \exp\left(-\frac{1}{2\sigma^2}\|r_i-w\|^2\right)$$ under a Gaussian likelihood. The MAP solution admits a closed-form,

$$w^* = (\Sigma_0^{-1} + N\sigma^{-2}I)^{-1} \left(\sigma^{-2} \sum_{i=1}^N r_i \right)$$

enabling efficient aggregation of environment-specific reward knowledge.

2. Domain Adaptation and Invariant Modeling

Reward modeling across domains necessitates mechanisms that prevent overfitting to domain-specific artifacts and instead capture truly generalizable preference signals. One formal strategy is domain-adversarial learning, exemplified by the DIAL framework (Wu et al., 1 Jan 2025), which optimizes a dual loss:

$$L_{\text{total}}(\theta,\phi,\psi) = L_{\text{src}}(\theta,\phi) + \lambda L_{\text{dom}}(\theta,\psi)$$

$L_{\text{src}}$ is a Bradley-Terry pairwise ranking loss on labeled source-domain data, and $L_{\text{dom}}$ measures distributional divergence—via the 1-Wasserstein distance—between source and target domains at the embedding layer. The critic $\psi$ enforces domain invariance; gradient penalties maintain the 1-Lipschitz constraint.

This approach supports cross-lingual transfer (English $\to$ Korean/Thai/Chinese; $+0.04\sim0.06$ accuracy gain) and cross-format or complexity (short$\to$long texts or few-shot$\to$full). Domain mixing ratios and regularization hyperparameters are tuned to maintain stability.

Another variant leverages sample reweighting under offline policy shift: in counterfactual ranking scenarios (Radwan et al., 29 Sep 2024), one assigns sample weights $w^k_i$ proportional to policy change propensities. The empirical loss is modulated to upweight data points of greater importance in target domains and penalize uneven fitting, minimizing the recovery coefficient of variation (Rec_cv) and outperforming vanilla IPS in recommender systems.

3. Model Architectures and Knowledge Integration

Cross-domain reward models manifest in several architectural paradigms:

• Linear aggregation: Given general and domain-specific reward models $R_g, R_i$, parameter interpolation yields $$R_{\text{merge}}(x,y) = \alpha R_g(x,y) + \sum_i \beta_i R_i(x,y)$$ (Lin et al., 1 Jul 2024). Parameter-level merging of transformers, followed by optional regularized fine-tuning, injects expert representations (e.g., numeracy circuits from a math LM) while maintaining general alignment.
• Router mechanisms: Lightweight architectures allow for modular routing—either internally via sparse mixture-of-experts (MoRE), externally by a classifier selecting among domain-specific reward models (RODOS), or by adapters within a single LLM (ARLISS) (Namgoong et al., 24 Jul 2024). This supports efficient parameterization, extension to new domains, and competitive binary preference accuracy (MoRE/ARLISS $\sim$0.70; baseline $\sim$0.6972).
• Multimodal fusion: Unified models such as UnifiedReward (Wang et al., 7 Mar 2025) and Skywork-VL Reward (Wang et al., 12 May 2025) integrate visual and textual embeddings, supporting both pointwise scoring and pairwise ranking for multimodal understanding, generation, and reasoning. Architectures typically consist of ViT-style visual embedders, transformer fusion layers, and shared reward heads.

4. Reward Signal Design Across Modalities

The efficacy of cross-domain models depends critically on reward signal construction:

• Verifiable and reasoning-consistent rewards: Encouraging both correctness and interpretable chain-of-thought (as in GRPO-based anti-spoofing (Jiang et al., 27 Jun 2025)) achieves cross-domain generalization; $$R_{\text{all}}(o) = R_{\text{format}} + R_{\text{cls}} + R_{\text{res}}$$, with reward terms for format, classification accuracy, and reasoning length.
• Partial/dense rewards: Multi-answer or high-sparsity tasks require reward shaping. For logical puzzles, partial correctness, format bonuses, or rescaled rewards enable learning where binary signals would collapse (Li et al., 23 Jul 2025).
• Preference strength measurement: The voting mechanism among reward model ensembles quantifies data quality, enabling filtering, label flipping, and adaptive margins to mitigate the impact of ambiguous or mislabeled data (Wang et al., 11 Jan 2024).
• Generative scoring: In RLVR frameworks for broad domains (medicine, chemistry, education, etc.), generative verifier LLMs produce soft reward signals calibrated by the model’s confidence distribution on correct answers (Su et al., 31 Mar 2025), which are normalized and used in policy optimization:

$\tilde r = \frac{r - \mu_r}{\sigma_r}$

5. Empirical Validation and Cross-Domain Transfer

Comprehensive experiments establish the validity of cross-domain reward modeling:

• Divide-and-conquer reward design in robot domains yields 51% faster, 85% easier user experience and 70% lower regret compared to joint tuning (Ratner et al., 2018).
• Counterfactual evaluation in ads ranking achieves a 17.6% Rec_cv reduction over vanilla IPS, indicating superior domain-adaptive reward estimation (Radwan et al., 29 Sep 2024).
• Merged and router-based models (DogeRM, MoRE/RODOS/ARLISS) systematically improve preference accuracy on domain-specific and general benchmarks (RewardBench: Math +30%, Code +6–8%, with minimal general task degradation) (Lin et al., 1 Jul 2024, Namgoong et al., 24 Jul 2024).
• Multimodal models set new state-of-the-art accuracy on VL-RewardBench and RewardBench (Skywork-VL Reward: 73.1%, 90.1%; UnifiedReward: up to 84% video understanding, 66.5% image understanding) (Wang et al., 12 May 2025, Wang et al., 7 Mar 2025).
• Cross-lingual transfer demonstrates $3$–$6$ percentage-point accuracy improvement over language-specific reward models and enhanced downstream instruction following ($+$9.5 pp win rate average) (Hong et al., 23 Oct 2024).
• Scalable RLVR for broad domains yields clear gains over base, supervised, and rule-based reward models (e.g., 62–65% math accuracy and 31% in multi-subject free-form QA), with generative verified signals enabling reliable performance on ambiguous and complex answers (Su et al., 31 Mar 2025).

6. Limitations and Open Questions

Despite advances, cross-domain reward modeling encounters several fundamental constraints:

• Transfer gaps: Domain shifts with non-overlapping features or modalities can diminish transfer quality; optimal merging or the choice of pivot domain remains an open question.
• Representation collapse: Reward models can inadvertently lose fine-grained domain-specific representations (cf. singular-value collapse diagnostics in cross-lingual transfer (Hong et al., 23 Oct 2024)).
• Adversarial instability: Domain-adversarial critic-based alignment (e.g., WDGRL, DIAL) may suffer from slow or unstable convergence.
• Sparse rewards and curriculum dynamics: Binary rewards can be inadequate for highly challenging or multi-step tasks; curriculum and staged training are necessary to prevent catastrophic forgetting (Li et al., 23 Jul 2025).
• Scaling and modality balance: Multimodal models are sensitive to dataset imbalance (e.g., limited video-gen pairs); parameter scaling and ongoing data collection are active research directions (Wang et al., 7 Mar 2025).
• Annotation costs and adaptation: Collecting paired cross-domain ground-truth can be prohibitive; semi-supervised or self-supervised alignment, efficient router architectures, and meta-learning for evolving policies are areas of vigorous investigation (Wang et al., 11 Jan 2024, Su et al., 31 Mar 2025).

7. Applications and Recommendations

Cross-domain reward models are foundational in multiple high-impact ML settings:

• Robotics: Efficient, scalable reward design enables generalized robot behavior in diverse operational contexts (Ratner et al., 2018).
• Recommender systems: Robust cross-domain reward estimation via domain adaptation improves evaluation and deployment of ranking models under offline policy shift (Radwan et al., 29 Sep 2024).
• Multimodal generation/understanding: Joint modeling across image, video, and text enhances synergy in generative and evaluative tasks (Wang et al., 12 May 2025, Wang et al., 7 Mar 2025).
• LLM alignment: Domain-invariant and merged reward heads support transfer across languages, styles, and specialized verticals (e.g., mathematics, code, legal).
• RL fine-tuning pipelines: Preference-strength weighted and meta-learned reward models maintain stability and generalization as the policy distribution shifts (Wang et al., 11 Jan 2024).

Best practices recommend divide-and-conquer reward specification for heterogeneous environments, Wasserstein domain-adversarial losses for alignment, modular router architectures for parameter efficiency and extensibility, and curriculum or staged reward shaping for multi-step or multi-answer reasoning tasks. Ongoing research targets richer cross-domain embedding spaces, automatic domain pivot selection, and scalable data-efficient preference annotation to drive continual improvement of general-purpose reward modeling frameworks.