Reward-Oriented Selection (ROSE)

• Reward-Oriented Selection (ROSE) is a framework that balances expected rewards against penalties and constraints, offering a principled approach for data and feature selection.
• ROSE employs diverse algorithmic strategies—such as network flows, dynamic programming, policy gradients, and influence functions—to tackle combinatorial optimization challenges.
• Empirical results demonstrate that ROSE improves efficiency, fairness, and robustness in applications like LLM tuning, feature curation, and RLHF pipelines.

Reward-Oriented Selection (ROSE) denotes a broad class of optimization and data selection methodologies that prioritize maximizing expected reward subject to explicit penalty terms, constraints, and performance metrics. ROSE encompasses diverse instantiations including feature selection in tabular learning, combinatorial set optimization, data curation for LLM instruction-tuning, reward model selection for personalized alignment, and active ratio-efficient annotation in RLHF pipelines. Across implementations, ROSE replaces traditional loss-based or heuristic-driven selection rules with reward-and-penalty-driven formulations, admitting algorithmic primitives from optimal stopping, combinatorial optimization, reinforcement learning, and influence-based or Fisher-information theoretic active learning.

1. Formal Definitions and Paradigms

Central to ROSE is the formulation of an objective that balances accumulated rewards against incurred penalties over a search or selection space. In combinatorial contexts, the canonical form is:

$$\max_{X\subseteq N}\;\Bigl\{\sum_{i: A_i\subseteq X}a_i \;-\;\sum_{j: B_j\cap X\neq\emptyset} b_j\Bigr\}$$

where $N$ is the universe, $\{A_i\}$ are reward-sets with weights $a_i\geq0$, and $\{B_j\}$ are penalty-sets with penalties $b_j\geq0$ (Heller et al., 2021). This generalizes set cover and hitting set, yielding the Reward-Penalty-Selection Problem (RPSP).

In automated feature selection and bias mitigation, the one-step ROSE reward evaluates:

$$R(s_t,a_t) = W - \sum_{f\in S_t\cap B}\psi - \sum_{\substack{f_b\in B,\;f_s\in S_t\\text{path exists in }G}} \mathbf1\{P(f_b,f_s)\}\frac{w(f_b,f_s)\lambda}{\ell(f_b,f_s)} + \sum_{f\in S_t\cap R}\rho + \phi(|S_t|)$$

where $W$ is predictive AUC, $\psi$ direct penalty for sensitive features, $\lambda$ controls indirect graph-based penalties, $\rho$ rewards desired features, and $\phi$ dynamically regularizes cardinality (Khadka et al., 9 Oct 2025).

In LLM instruction data selection, ROSE computes for each training example $z$ an influence score:

$$S(z)\approx \bigl\langle\nabla_\theta L_{\rm val}(\theta),\,\nabla_\theta \ell(z;\theta)\bigr\rangle$$

quantifying the first-order impact of $z$ on downstream preference loss (Wu et al., 2024).

2. Algorithmic Strategies and Computational Frameworks

Algorithmic instantiations of ROSE fall into several families:

• Network Flow and Min-Cut: Max-RPSP admits a solution via a single min-cut in a bipartite network encoding reward and penalty sets (Heller et al., 2021).
• Dynamic Programming: For laminar set families and bounded tree-width variants, dynamic programs construct optimal selections by exploiting the structure of induced graphs, yielding tractability (Heller et al., 2021).
• Policy Gradient and Reinforcement Learning: In feature selection, the agent operates over binary mask state spaces, parameterizes the policy via MLP, and optimizes expected episode reward using REINFORCE (Khadka et al., 9 Oct 2025).
• Influence Function Approximations: ROSE for data selection employs first-order gradients of a preference-driven loss to estimate the utility of each candidate example, avoiding expensive Hessian inversion (Wu et al., 2024).
• Fisher Information Maximization: For active reward model annotation, the D-optimal ROSE selects pairs that maximize the determinant of accumulated Fisher information, operationalized by embedding differences and response uncertainty (Shen et al., 4 Feb 2025).
• Optimal Stopping: Sequential ROSE settings reduce to thresholding constructed independent reward random variables, with explicit backward recursion yielding memoryless stopping policies (Goldenshluger et al., 2019).

3. Integration with Downstream Systems and Reward-Driven Evaluation

ROSE is designed for modularity, integrating with non-differentiable evaluators (e.g., tree ensembles) and downstream learning protocols. In feature selection, ensemble models serve as black-box oracles for predictive validation (AUC), fully decoupled from the RL core (Khadka et al., 9 Oct 2025). In LLM alignment, annotated pair selection propagates through reward model retraining and policy fine-tuning (Shen et al., 4 Feb 2025). ROSE-based data selection leverages the selected data subset for LoRA or full SFT fine-tuning, directly modulating downstream win-rate metrics (Wu et al., 2024).

A key advance in personalized alignment is the decoupling of proxy reward model accuracy (RM-Acc) from actual sequence-level generation outcomes (Policy-Acc), with direct behavioral benchmarks (Pref-LaMP) revealing no monotonic gains from higher RM-Acc; thus, ROSE system design requires validation against ground-truth completions rather than surrogate win-rate (Rezk et al., 28 Dec 2025).

4. Bias Mitigation, Regularization, and Fairness

ROSE incorporates multi-component regularization and fairness constraints. The graph-based indirect bias penalty in feature selection considers all paths from protected features across correlation networks, penalizing both direct and latent leakage (Khadka et al., 9 Oct 2025). Dynamic cardinality regularization is enforced by shaping subset size penalties, with annealing options for time-varying regularization schedules. In combinatorial regimes, penalty frequency and set interactions are bounded either by laminarity or tree-width for efficient optimization (Heller et al., 2021).

Empirically, ROSE-driven feature selection demonstrates decreased cumulative penalty (e.g., $P_\mathrm{total} \approx 20$ vs. baselines $>30$) and stable convergence to compact, bias-minimized subsets (Khadka et al., 9 Oct 2025).

5. Empirical Results and Benchmark Comparisons

Across domains, ROSE consistently yields superior or more efficient selection relative to legacy strategies. In feature selection on the Home Credit Default Risk dataset, ROSE achieved AUC $\approx 0.75$ versus $0.70$ (Random Forest, all features) and $0.65$ (Logistic Regression, handpicked) (Khadka et al., 9 Oct 2025). ROSE-selected LLM instruction data (5% subset) surpassed full-dataset fine-tuning by $+9.3$ to $+6.8$ pp in win-rate across three benchmarks (SHP, SE, HH), outperforming similarity and CE-based methods (Wu et al., 2024). Active annotation with Fisher-ROSE achieved equal test performance with up to $50\%$ fewer annotations, robustness to hyperparameter variation, and pronounced gains when cross-prompt comparisons were exploited (Shen et al., 4 Feb 2025).

In policy selection for LLM deployment, reward-guided decoding methods did not scale with model size past $3$B parameters; in-context learning (ICL-RAG) delivered $+2.9$–$3.1$ ROUGE-1 improvement over reward-based methods at $7$B scale, with behavioral metrics (ROUGE-1, BERTScore) decoupled from RM-accuracy (Rezk et al., 28 Dec 2025).

6. Complexity and Tractability

ROSE's computational tractability is governed by the structure of reward and penalty constraints. Polynomial-time solvability results are established for max-regimes (min-cut) and laminar or tree-width-bounded set families (dynamic programming, IP) (Heller et al., 2021). NP-completeness afflicts the general min-regime, e.g., reductions from Maximum Independent Set where singleton rewards and size-2 penalties yield intractability. Subgraph generalizations (SGSP) on trees with bounded penalty frequency admit polynomial IP-solvers. Influence-based and Fisher criteria introduce $O(Jd^2 + d^3)$ complexity per annotation round, negligible compared to human labeling latency in practice (Shen et al., 4 Feb 2025).

7. Connections, Generalizations, and Research Directions

ROSE serves as a unifying abstraction for problems embedding reward-maximization under explicit penalty consideration, subsuming set cover/hitting-set, feature selection, RLHF annotation, and sequential optimal stopping. It admits further generalization: any universe $N$ endowed with reward/penalty constraints as arbitrary predicates over $2^N$ (with associated weights) yields a valid ROSE instance (Heller et al., 2021). Algorithmic tools—network flows, DP, IP on interaction graphs, policy gradients—apply provided incidence graph structure is amenable. Empirical and theoretical analyses suggest continued advancement in ROSE frameworks for robust, efficient, and fair selection under composite objective landscapes.