Unifying and Optimizing Data Values for Selection via Sequential-Decision-Making (2502.04554v1)

Abstract: Data selection has emerged as a crucial downstream application of data valuation. While existing data valuation methods have shown promise in selection tasks, the theoretical foundations and full potential of using data values for selection remain largely unexplored. In this work, we first demonstrate that data values applied for selection can be naturally reformulated as a sequential-decision-making problem, where the optimal data value can be derived through dynamic programming. We show this framework unifies and reinterprets existing methods like Data Shapley through the lens of approximate dynamic programming, specifically as myopic reward function approximations to this sequential problem. Furthermore, we analyze how sequential data selection optimality is affected when the ground-truth utility function exhibits monotonic submodularity with curvature. To address the computational challenges in obtaining optimal data values, we propose an efficient approximation scheme using learned bipartite graphs as surrogate utility models, ensuring greedy selection is still optimal when the surrogate utility is correctly specified and learned. Extensive experiments demonstrate the effectiveness of our approach across diverse datasets.

• The paper introduces a novel framework that formulates data selection as a finite-horizon deterministic Markov Decision Process for systematic optimization.
• It leverages dynamic programming and approximate techniques, including a bipartite graph approximation, to address the limitations of traditional myopic data valuation methods.
• The empirical and theoretical results demonstrate enhanced model training efficacy and resource efficiency across diverse benchmark datasets.

Unifying and Optimizing Data Values for Selection via Sequential-Decision-Making

The paper "Unifying and Optimizing Data Values for Selection via Sequential-Decision-Making" presents a novel framework for advancing data selection methodologies through a sequential decision-making lens. This research addresses a critical aspect of machine learning—optimal data selection—by evaluating the contributions of individual data points, demonstrating that this problem can be effectively modeled as a sequential decision-making process. The authors propose a framework that reformulates data selection as a deterministic Markov Decision Process (DMDP), leveraging dynamic programming (DP) and approximate dynamic programming (ADP) techniques.

Framework and Methodology

The conventional data valuation methods documented in the literature, such as Data Shapley, are scrutinized and reinterpreted within the proposed sequential decision-making framework. The authors reveal the inherent limitations of current methods when precision and optimality in data selection are necessary, particularly under conditions of submodularity with curvature constraints.

In their framework, the paper outlines a new formulation of data selection as a sequential decision-making optimization challenge. It is achieved by evaluating data values through cumulative utility across all possible subset sizes. This perspective not only unveils better alignment with theoretical optimization principles but also opens avenues for more systematic and effective solutions through dynamic programming, directly optimizing the sequential utility aggregation.

Key Contributions

1. Sequential Decision Formulation: The problem is rigorously defined and structured as a finite-horizon Deterministic Markov Decision Process, enabling a direct application of dynamic programming principles.
2. Approximate Dynamic Programming Analysis: The authors dissect existing data valuation methods, revealing that many can be viewed through approximative lenses as methods using myopic policies—short-sighted strategies that prioritize immediate rewards without considering long-term effects.
3. Bipartite Graph Approximation: Given the computational complexities of the exact DP solutions, an efficient bipartite graph-based approximation is proposed. This method reduces computational effort while maintaining critical utility dependencies, enabling near-optimal selections.
4. Theoretical and Empirical Evaluation: The proposed method is analyzed both theoretically and empirically, showing substantial improvements over traditional methods on a range of standard benchmark datasets.

Experimental Evidence and Implications

The paper demonstrates empirically that the proposed ADP-based solutions frequently outperform existing methods. Through extensive experimentation across datasets with varying properties, the authors establish the practical benefits of their approach. Moreover, the method's theoretical soundness is corroborated by proofs demonstrating that the greedy policies derived through the proposed approximations retain optimal or near-optimal qualities under the derived framework.

The implications of this research are profound. By bridging a gap between theoretical optimality and computational feasibility, the framework equips researchers and practitioners with tools to perform more effective data selection. It not only enhances model training efficacy but also contributes to resource-efficient machine learning workflows, which are crucial for handling increasingly large datasets without proportional growth in computational resources.

Future Directions

The work opens multiple avenues for further research, notably the exploration of even more sophisticated ADP techniques and deeper integration with complex utility structures and feedback loops. As AI systems become more ingrained in diverse domains, the need for refined data selection processes that balance efficiency and performance will continue to grow.

The discourse this paper initiates could lead to innovative intersections between data evaluation, combinatorial optimization, and machine learning, yielding strategies that enhance the efficacy of AI systems across ever-expanding application fields.