Customizable Reward Functions Overview

• Customizable reward functions are flexible objective models in reinforcement learning that can be parameterized and adapted to meet diverse stakeholder goals.
• Recent approaches leverage preference-conditioned neural networks, programmatic DSLs, and curriculum-based strategies to dynamically adjust rewards during training.
• Empirical results demonstrate enhanced sample efficiency, improved policy optimality, and robust multi-objective performance in human-in-the-loop and risk-aware settings.

Customizable reward functions are a foundational tool in reinforcement learning (RL), sequential decision-making, and machine learning systems requiring behavioral alignment. The principal goal of customizable reward design is to endow an RL agent or a judgment model with an objective function whose structure, weights, or evaluation criteria can be tailored—before or during training—to suit the needs of particular stakeholders, tasks, or user groups. Recent developments span a wide spectrum: explicit parametric schemes, preference-conditioned neural networks, program synthesis, and domain-specific interpretable reward architectures. This article surveys the technical principles, methodologies, and empirical results underlying customizable reward functions, with focus on recent advances across RL, LLM preference modeling, multi-objective and risk-aware control, and human-in-the-loop scenarios.

1. Formal Frameworks for Customizable Reward Functions

Customizability in reward functions generally entails the capacity to parameterize the reward in ways that are aligned with diverse objectives, user preferences, or operational constraints. Common formalizations include:

• Linear multi-objective reward scalarization: The reward at each timestep is a linear combination of feature channels, $r(s_t, a_t) = w^\top \phi(s_t, a_t)$, with user-supplied or learned weight vector $w$ (Friedman et al., 2018). Conditioning the policy and critic on $w$ allows for generalization across the simplex of possible objectives without retraining.
• Modular risk-return objectives: In finance and other domains, reward may be a weighted sum/difference of return, risk, and performance ratios (e.g., Sharpe, Treynor), $R(\theta) = w_1 R_1 - w_2 R_2 + \dots$, with weights $w_i$ set through grid search or meta-optimization to match investor profiles (Srivastava et al., 4 Jun 2025). Each term is differentiable in policy parameters and can be tuned independently.
• User-specific preference models: Reward models can be designed to map user, domain, or criterion metadata into reward conditionings, supporting calibrated alignment to individualized or group-level preferences (Jia et al., 13 Aug 2025, Cheng et al., 2023).
• Programmatic and symbolic reward DSLs: DSL-based schemes enable designers to express multi-stage or subgoal-based reward via logic programs with parameter holes, which are then filled to optimize fit to demonstrations (Zhou et al., 2021) or whose execution can be conditioned at runtime (Donnelly et al., 17 Oct 2025).
• Dynamic/interactively learned reward vectors: User or group behavior (e.g., via system logs or pairwise preferences) is modeled as the consequence of an unknown reward, which is inferred via maximum entropy inverse RL (Li et al., 2017) or preference-based neural methods (Katz et al., 2021).

The spectrum of customizability thus spans parameter vectorization, modular architectures, context-sensitive adaptation, and full programmatic specification.

2. Customization Methodologies and Algorithms

Recent literature has introduced both general recipes and domain-specific pipelines for reward customization, including:

• LLM-driven reward synthesis via progress functions: Instead of handcrafting dense rewards, a LLM synthesizes a progress function $P(s)$ from a task description and observation schema. This coarsely estimates how far an agent is along a trajectory. Once $P(s)$ is available, it is discretized and coupled with count-based intrinsic novelty rewards, yielding a compositional pipeline where forward progress and novelty can be tuned independently and generalized across new tasks without per-task weight tuning (Sarukkai et al., 2024).
• Curriculum reward composition: Multi-stage curricula decompose intricate rewards into coarse proxies (e.g., goal, velocity) and full complex compositions, transferring from simple to complex rewards automatically based on policy convergence metrics (e.g., critic-fit loss). Flexible replay buffers allow immediate re-use of experiences across reward settings (Freitag et al., 2024).
• Conditional deep RL (hyper-policy) for reward sensitivity: By augmenting the observation input with a conditioning vector $c$ (encoding reward weights), a policy can learn to produce behavior aligned with any value of $c$ in a near-optimal subspace, thus enabling post-hoc reward specialization or on-the-fly policy steering without retraining (Wei et al., 2021).
• Preference-based reward repair and adaptation: When a misspecified proxy reward $R_p$ leads to "reward hacking," preference-based correction frameworks iteratively learn a transition-dependent $\Delta R$ from a minimal set of human preferences over targeted trajectory pairs, repairing only the transitions that matter for policy optimality (Hatgis-Kessell et al., 14 Oct 2025).
• Inverse RL from user behavior logs: Empirical interaction traces yield feature-weighted user-specific reward vectors $\theta$, which adapt as new user logs/contexts accumulate, enabling fully differentiated system behaviors per user/group (Li et al., 2017).
• Data-driven reward re-ranking via Pareto-dominance: In domains such as drug design, reward functions are learned entirely from multi-objective experimental data by fitting a neural net to reproduce ground-truth Pareto preferences, automatically discovering normalization and aggregation parameters without manual tuning (Urbonas et al., 2023).

These approaches decouple the challenge of "what to reward" (structure, criteria, weights) from "how much to reward," often by transferring the latter to data-driven or procedural optimization.

3. Architectures and Models for Preference-Conditioned Rewards

Several architectures support explicit customizability at inference time:

• Reward models with criterion-conditioning: Models such as the Customizable Reward Model (CRM) prepend natural-language user criteria to the input and pairwise score responses, learning to respect new criteria not seen during training. Empirical results show near-complete transfer to topic and criterion generalization benchmarks, including strong robustness to noised or contradictory criteria (Jia et al., 13 Aug 2025).
• Multi-head and criterion/weight injection in LLMs: For highly structured evaluations (e.g., radiology report grading), models output a vector of sub-rewards, then aggregate to a total via user-specified weights. Margin-based losses calibrate both sub-criteria and total margin, enabling interpretable, weighted customization (Liu et al., 2024).
• Neural feature augmentation: Preference-based architectures extend standard feature-based reward models with additional neural feature channels, which can discover and encode user-specific preferences that hand-coded features miss. Slicing these neural features reveals interpretable structure for customization (Katz et al., 2021).
• Automatic input conditioning and data augmentation: Reward models can be trained via multi-stage curricula, where initial general calibration is followed by targeting domain-specific (customized) preferences, with combined imitation and ranking losses preserving global and personalized capabilities (Cheng et al., 2023).

These architectures achieve both invariance (global task alignment) and adaptation (local customization), without requiring model re-training for each new set of substantive preferences.

4. Practical Design Patterns and Empirical Guidelines

Empirical studies consistently highlight the importance and effectiveness of practical reward customization recipes:

• Divide-and-conquer reward design: Specifying proxy rewards independently per environment (when task decomposability allows) leads to lower solution regret, greater subjective ease-of-use, and faster user convergence relative to joint reward tuning, especially when each environment lacks full feature coverage (Ratner et al., 2018).
• Risk-aware and modular objectives: In financial RL, modular composite rewards allow practitioners to trace out risk-return frontiers by grid or meta-optimization over weights, and to extend the reward with additional risk terms (e.g., CVaR, drawdown) as needed (Srivastava et al., 4 Jun 2025).
• Barrier and shape-based augmentation: In safety-critical applications, reward customization via potential-based log-barriers enforces state constraints without altering optimal policies, yielding faster convergence and reduced actuation in robot learning (Nilaksh et al., 2024).
• Programmatic and symbolic customization: Domain-specific languages (DSLs) or runtime monitoring frameworks (e.g., RML) enable arbitrary non-Markovian, data-parameterized, and memory-dependent customizations, with exponentially greater expressivity than finite-state automata, facilitating more compact and interpretable reward specifications (Zhou et al., 2021, Donnelly et al., 17 Oct 2025).
• Recursive aggregation functions: Rather than alter per-step reward, the aggregation function (e.g., discounted-max, mean, Sharpe ratio) can be customized and recursively computed, inducing entirely different agent risk behaviors and objectives without changing the core reward signal (Tang et al., 11 Jul 2025).

Best-practice recommendations include starting with interpretable feature sets, conditioning on user/environment context when possible, favoring data-driven or programmatic adaptation over repeated hand-tuning, and using reward-aggregation or auxiliary criteria aligned with the evaluation metric.

5. Empirical Impacts and Performance Guarantees

Across benchmarks, customizable reward function strategies consistently yield substantial improvements in:

• Sample efficiency: LLM-generated progress functions and count-based bonuses yield $20\times$ savings in full RL runs on the Bi-DexHands benchmark relative to prior SOTA (Sarukkai et al., 2024). Reward repair with targeted feedback dramatically reduces required preferences compared to proxy-free RLHF (Hatgis-Kessell et al., 14 Oct 2025).
• Policy optimality and behavioral diversity: In multi-objective and personalized settings, conditioning on reward weights or criteria allows for post hoc behavioral adjustment and robust generalization, with negligible loss in absolute performance (Friedman et al., 2018, Jia et al., 13 Aug 2025).
• Alignment and robustness: CRM and multi-criterion LLM schemes maintain high correlation with human judgments, retaining near-perfect accuracy amid contradictory or incomplete user input, even outperforming leading proprietary models on several metrics (Jia et al., 13 Aug 2025, Liu et al., 2024).
• Interpretability and user satisfaction: Divide-and-conquer and programmatic approaches increase subjective ease-of-use and reduce tuning effort, as confirmed by user studies in both abstract and realistic environments (Ratner et al., 2018, Zhou et al., 2021).

Bounded regret and policy invariance results are established in several repair and shaping schemes, ensuring that accelerating learning or enforcing structure does not compromise asymptotic performance (Hatgis-Kessell et al., 14 Oct 2025, Nilaksh et al., 2024, Devidze, 27 Mar 2025).

6. Limitations, Open Challenges, and Future Directions

Despite these advances, several challenges remain for customizable reward function design:

• Scalability in high-dimensional or continuous spaces: As the number of objectives or features grows, standard parameterizations may suffer from coverage gaps; active-sampling, embedding, or curriculum strategies are required (Friedman et al., 2018).
• Credit assignment and preference collection: Learning from localized or segment-level preferences, rather than full trajectories, as well as properly identifying the minimal set of reward corrections, remains an open technical and HCI problem (Hatgis-Kessell et al., 14 Oct 2025).
• Expressiveness and automation trade-offs: While DSLs and symbolic machines offer maximal expressivity, they may require expert specification; LLMs and neural models can automate progress estimation but may miss subtle task nuances (Sarukkai et al., 2024, Donnelly et al., 17 Oct 2025).
• Generalization under user/group shifts: Domain adaptation and robustness to nonstationary or rarely seen preferences require careful regularization and noising during training (Jia et al., 13 Aug 2025).
• Alignment guarantees: There remains a gap between proxy reward specification and actual realization of human intent, especially when preferences are conflicting or ambiguous across user groups (Li et al., 2017, Cheng et al., 2023).

Ongoing research targets meta-learning over reward weights (Srivastava et al., 4 Jun 2025), modular plug-and-play criterion heads (Liu et al., 2024), and scalable IRL for large interactive systems (Li et al., 2017), all with the goal of further automating the synthesis and alignment of reward functions to truly customizable, human-centric objectives.