Summary of Closing the Gaps: Optimality Of Sample Average Approximation For Data-driven Newsvendor Problems, by Jiameng Lyu et al.
Closing the Gaps: Optimality of Sample Average Approximation for Data-Driven Newsvendor Problems
by Jiameng Lyu, Shilin Yuan, Bingkun Zhou, Yuan Zhou
First submitted to arxiv on: 6 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary We investigate the regret performance of Sample Average Approximation (SAA) for newsvendor problems with convex inventory costs. In literature, the optimality of SAA has not been fully established under specific conditions. This paper bridges the gap between upper and lower bounds for both conditions. Under local strong convexity, we prove an optimal regret bound of O(log T/α + 1/(αβ)) for SAA, showing that its long-term regret performance is influenced only by α and not β. We also propose a new gradient approximation technique and smooth inverted-hat-shaped hard problem instances that can be used for lower bounds in broader data-driven problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how well Sample Average Approximation (SAA) works in making decisions about inventory levels. SAA is a way to make predictions based on past data, but its performance hasn’t been fully understood. The authors fill in the gaps between upper and lower bounds for different conditions. They show that under certain circumstances, SAA’s long-term performance only depends on one factor (α) and not another (β). This helps us understand how local properties affect SAA’s regret performance. |
