The Value of Randomized Strategies in Distributionally Robust Risk-Averse Network Interdiction Problems
Bibliographic record
Abstract
Conditional value at risk (CVaR) is widely used to account for the preferences of a risk-averse agent in extreme loss scenarios. To study the effectiveness of randomization in interdiction problems with an interdictor that is both risk- and ambiguity-averse, we introduce a distributionally robust maximum flow network interdiction problem in which the interdictor randomizes over the feasible interdiction plans in order to minimize the worst case CVaR of the maximum flow with respect to both the unknown distribution of the capacity of the arcs and the interdictor’s own randomized strategy. Using the size of the uncertainty set, we control the degree of conservatism in the model and reformulate the interdictor’s distributionally robust optimization problem as a bilinear optimization problem. For solving this problem to any given optimality level, we devise a spatial branch-and-bound algorithm that uses the McCormick inequalities and reduced reformulation linearization technique to obtain a convex relaxation of the problem. We also develop a column-generation algorithm to identify the optimal support of the convex relaxation, which is then used in the coordinate descent algorithm to determine the upper bounds. The efficiency and convergence of the spatial branch-and-bound algorithm is established in numerical experiments. Further, our numerical experiments show that randomized strategies can have significantly better performance than optimal deterministic ones. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: The first author’s research is supported by a Group for Research in Decision Analysis postdoctoral fellowship and Fonds de Recherche du Québec–Nature et Technologies postdoctoral research scholarship [Grants 275296 and 301065]. The second author acknowledges support from the Canadian Natural Sciences and Engineering Research Council and the Canada Research Chair program [Grants RGPIN-2016-05208, 492997-2016, and 950-230057]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.1257 . The data file and codes are posted on GitHub ( https://github.com/Utsav19/Value-of-Randomization ).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".