Domain-Informed Reward Signals

• Domain-informed reward signals are explicitly engineered supervision signals that integrate expert domain knowledge to guide RL and RLHF, ensuring improved efficiency and alignment.
• They employ methods like teacher-driven design, automata-based construction, and model merging to embed domain constraints and structured feedback into learning frameworks.
• Empirical results demonstrate accelerated convergence, enhanced generalization, and reduced reward hacking across diverse applications in both physical and digital domains.

Domain-informed reward signals are scalar or structured supervision signals in reinforcement learning (RL) or RL-from-human-feedback (RLHF) settings that are explicitly constructed—by direct engineering or by integrating domain knowledge—so as to encode expert assumptions, constraints, or desirable macroscopic behaviors of the underlying task domain. Their primary function is to improve efficiency, stability, generalization, and alignment of RL agents or LLMs, especially when sparse, ambiguous, or noisy native environment signals are insufficient, or when domain-specific correctness and process-level fidelity are critical.

1. Formal Definitions and Foundations

A domain-informed reward signal $R'$ is a judiciously crafted function (or structured automaton) that integrates domain knowledge into the RL objective:

• In standard RL, the agent seeks $$\pi^* = \arg\max_\pi \mathbb{E}\big[\sum_t \gamma^t R(s_t,a_t)\big]$$ for reward $R(s,a)$ delivered by the environment. In domain-informed RL, $R'(s,a)$ is constructed using knowledge of optimal policies $\pi^*$, subgoals, invariants, or interpretable order parameters, to guide learning toward globally optimal or structurally desirable solutions (Devidze, 27 Mar 2025).
• In RLHF for LLMs, reward modeling typically replaces human preference annotation with a reward model $r_\phi(x,y)$ trained on paired (chosen/rejected) samples. Domain-informed reward models encode domain-specific structure (via feature engineering, programmatic checking, or weight merging with specialist models) to reflect task priorities not captured by generic preference data (Lin et al., 2024, Nath et al., 2024).

The essential property is that $R'$ encodes domain structure, constraints, or expert priors that accelerate convergence and avoid spurious optima typical of sparse or misaligned signals (Devidze, 27 Mar 2025, Straat et al., 31 Oct 2025).

2. Design Methodologies for Domain-Informed Rewards

2.1. Teacher-Driven and Algorithmic Construction

Teacher-driven approaches design $R'$ analytically, encoding knowledge of $\pi^*$ or $V^*$ (optimal value function) and subgoals into local or potential-based rewards. Non-adaptive designs select a sparse set of subgoals $Z$ and ensure Bellman-optimality invariance for all optimal policies, then maximize informativeness by creating stepwise reward gaps favoring optimal over suboptimal actions. Adaptive interpretable shaping further tailors $R'$ at each round based on current policy performance, maintaining alignment and sample efficiency (Devidze, 27 Mar 2025).

Algorithmic and automata-based construction uses reward machines—finite automata specified with propositional event detectors and transition-driven rewards—to encode subtask progression and domain-specific workflows. As exemplified in knowledge-informed penetration testing, events drawn from domain ontologies (e.g., MITRE ATT&CK) govern reward emissions at each POMDP transition; more detailed automata yield greater sample efficiency and agent interpretability (Li et al., 2024).

2.2. Integration via Model Architecture and Merging

For LLM reward modeling, domain-informed model merging (as in DogeRM) blends a general reward model (trained on broad preference data) with a supervised domain-specific specialist via layerwise linear interpolation. Only a small amount of domain SFT data is required; blockwise merging preserves the robust head of the general model but injects domain logic into embeddings and transformer layers, balancing generalization and domain alignment (Lin et al., 2024). Adaptive grid search over mixture coefficient $\alpha$ controls the general-domain tradeoff.

Modular architectures with domain routers—such as mixtures-of-experts (MoRE), router-plus-adapters (ARLISS), or external routers with banks of domain reward models (RODOS)—allow the reward model system to specialize segments of the model or entire sub-models to particular domains, under the control of data-driven or explicitly-trained routing mechanisms. This yields parameter-efficient, robust, and extensible reward modeling (Namgoong et al., 2024).

2.3. Structured and Automated Rubric/Criteria-Based Signals

Advanced frameworks use rubrics—systematically generated criteria from reference solutions—to define dense, fine-grained, domain-specific rewards. For each prompt-task pair, rubrics comprise factual and process items (with learned weights), and rewards are computed as weighted satisfaction of these items. This approach enables interpretable, generalizable feedback across heterogeneous reasoning domains such as mathematics, physics, and general QA (Bi et al., 15 Nov 2025).

Process reward models (PRMs), as in Fin-PRM, formalize step-level and trajectory-level rewards by aggregating signals of importance, qualitative judgement, and domain-anchored accuracy at each reasoning step and for the entire trajectory, with weights and aggregation tuned to encode task priorities and factual coverage (Zhou et al., 21 Aug 2025).

2.4. Domain Knowledge from Programmatic or Knowledge-Graph Supervision

Domain-informed reward signals can be extracted automatically from structured knowledge sources such as knowledge graphs. For compositional reasoning, path-derived rewards score the model’s chain-of-thought by coverage and alignment against reference KG paths, using graded coverage, repetition penalties, and minimum-hit constraints for verifiable and tamper-resistant process-level supervision (Kansal et al., 21 Jan 2026).

Similarly, in RLVR frameworks for LLMs, verifiable reward models are trained to deliver binary or confidence-weighted scores based on cross-domain reference answers, with reward signals normalized within training batches. This generalizes reward verification beyond math/code into less structured scientific or social domains, leveraging consistency across expert-written references (Su et al., 31 Mar 2025).

3. Empirical Impact: Efficiency, Generalization, and Alignment

Sample and training efficiency: Domain-informed signals consistently accelerate convergence. For example, DogeRM merging general RM with a math-tuned SFT model yields +11–17% accuracy on reasoning tasks, outperforming models trained from scratch or with naive finetuning (Lin et al., 2024). Physics-informed RL for convective flows achieves Nusselt number reductions up to 33% laminar (vs. 10% for conventional control) and generalizes robustly to chaotic regimes (Straat et al., 31 Oct 2025).

Complex, domain-rich environments: Reward machines based on detailed domain ontologies in penetration testing reduce training steps and evaluation action counts by 2–3× compared to scalar reward baselines, with the richer automata giving superior interpretability and efficiency (Li et al., 2024).

Scalability and robustness: Modular and router-based architectures achieve comparable or better performance to monolithic models, while reducing parameter footprint by up to 55% (Namgoong et al., 2024). Rubric-guided RL outperforms final-answer or naive text-similarity rewards by +5–8% in multi-domain benchmarks and breaks through exploration bottlenecks that constrain single-signal RL (Bi et al., 15 Nov 2025).

Interpretability: Feature-based reward modeling (e.g., 7 interpretable features for opinion summarization) enables local sensitivity analysis and matches or surpasses SOTA with $>20\times$ reduction in preference labeling requirement, confirming the benefit of explicit domain encoding for human-aligned tasks (Nath et al., 2024).

4. Theoretical and Algorithmic Properties

Potential-based shaping and invariance: Potential-based domain-informed rewards theoretically preserve the original optimality (Bellman invariance) and speed up exploration by aligning the reward structure with optimal value gaps. Adaptive and meta-learned shaping procedures further refine signals to be informative with respect to the current policy, with convergence guarantees under certain conditions (Devidze, 27 Mar 2025).

Avoiding overfitting and reward hacking: Interpolating domain-specific logic with general models prevents catastrophic forgetting and overfitting to small or biased domain datasets (Lin et al., 2024). Composite rewards constructed with multi-criteria rubrics or KG-paths, empirically and by design, restrict reward hacking by requiring multi-level alignment (process and outcome) (Bi et al., 15 Nov 2025, Kansal et al., 21 Jan 2026).

Domain adaptation and transfer: Domain-invariant reward models, optimized by adversarial losses to align source and target feature distributions, enable transfer of human preference signals across language, style, and complexity domains. This provides a principled basis for generalizing domain-informed signals via distribution-matching losses (e.g., Wasserstein) (Wu et al., 1 Jan 2025).

5. Applications Across Domains

The utility of domain-informed reward signals is demonstrated across:

• RL for physical/engineering control: Stabilization of chaotic flows (Straat et al., 31 Oct 2025), physics-informed diffusion model generation by enforcing global PDE residual minimization (Yuan et al., 24 Sep 2025).
• RLHF for LLMs: Opinion summarization, with domain-specific feature vectors and small annotation budgets (Nath et al., 2024); mathematics/coding/medical/chemistry/financial reasoning, via rubrics, reward merging, or knowledge graph supervision (Bi et al., 15 Nov 2025, Kansal et al., 21 Jan 2026, Zhou et al., 21 Aug 2025).
• Autonomous cybersec task learning: Penetration testing with event-driven automata rewards enables efficient, interpretable, and scalable policy discovery (Li et al., 2024).
• Subjective generation tasks: Narrative story generation guided by literary theory-based reward rubrics and group-relative advantage (Liu et al., 23 Jan 2026).
• Continuous domain adaptation: Reinforcement-learned domain-selection paths using unsupervised embedding-distance rewards to optimize transfer learning in representation space (Liu et al., 12 Oct 2025).
• Biological learning analogs: Evolutionary trajectories from reward-driven learning to reward-agnostic, domain-adapted plasticity in neuromodulated NNs, resulting in orders-of-magnitude improvement in learning efficiency (Arnold et al., 2024).

6. Challenges, Limitations, and Open Directions

Expert signal acquisition: Teacher-driven or rubric-based reward design requires strong domain knowledge and may not scale to all domains, particularly where explicit optimal policies are unavailable or rubric items are difficult to formalize (Devidze, 27 Mar 2025, Bi et al., 15 Nov 2025).

Reward model transfer and compositionality: Balancing specialization with generalization remains non-trivial. Router-based models and blockwise merging provide partial composability, but domain-invariant reward learning and process-level reward aggregation are active research areas (Namgoong et al., 2024, Wu et al., 1 Jan 2025).

Faithfulness, reward hacking, and interpretability: Ensuring that domain-informed rewards cannot be exploited or gamed (e.g., process-coverage vs. content) continues to motivate research into layered rubrics, hybrid outcome/process rewards, and transparent automata-based supervision (Bi et al., 15 Nov 2025, Li et al., 2024).

Automated domain-informed reward synthesis: Future work outlined includes automated rubric/item weight learning, hierarchical rubrics for complex tasks, meta-learning of reward templates, and extensions to multi-modal or underspecified domains (Bi et al., 15 Nov 2025, Zhou et al., 21 Aug 2025).

7. Practical Guidelines and Best Practices

Collect SFT or domain-specific data wherever feasible; use cheap synthetic SFT for new domains (Lin et al., 2024).

Explicitly encode order parameters, subgoals, or domain invariants in reward functions; use potential-based or automata-based shaping where process structure is available (Straat et al., 31 Oct 2025, Li et al., 2024).

When scaling across domains, exploit modular architectures or router-based designs for extensibility and robustness (Namgoong et al., 2024).

For domains with structured references, leverage verifiable and knowledge-derived rewards for compositional and interpretable process supervision (Kansal et al., 21 Jan 2026, Su et al., 31 Mar 2025).

Balance domain and general signals (e.g., via interpolation or regularization), and tune mixture/hyperparameters on held-out validation sets (Lin et al., 2024, Yuan et al., 24 Sep 2025).

In summary, domain-informed reward signals provide a principled, empirically validated, and theoretically grounded methodology for embedding domain expertise, process fidelity, and task-specific desiderata into RL and LLM training pipelines, enabling robust, efficient, and interpretable learning in complex real-world domains.