Reproduce “The Curvature of Regret in Contextual Linear Optimization” on OpenResearch
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About this paper
Konstantinos Ziliaskopoulos, Alexander Vinel, Alice E. Smith
The paper derives a geometric formula for how population regret changes under small cost-prediction errors in contextual linear optimization. Although an individual linear-programming decision can change discontinuously, average regret grows quadratically near the optimum; the resulting curvature also guides scenario allocation, reducing battery-arbitrage regret by 30.8% versus uniform allocation in the reported experiment.
Key insights
- Averaging over costs smooths the effect of a discontinuous optimizer: small perturbations produce regret proportional to the square of their size, with curvature concentrated on decision boundaries.
- Prediction errors parallel to a boundary do not contribute to crossing it; the decision impact depends on the direction of error as well as its magnitude.
- One projection-based calculation provides a tractable approximation to the geometric curvature, which can prioritize sampling where uncertainty is most likely to change decisions.
Summary by alphaXiv.
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