Approximation Algorithms for Distributionally Robust Stochastic\n Optimization with Black-Box Distributions
Bibliographic record
Abstract
Two-stage stochastic optimization is a framework for modeling uncertainty,\nwhere we have a probability distribution over possible realizations of the\ndata, called scenarios, and decisions are taken in two stages: we make\nfirst-stage decisions knowing only the underlying distribution and before a\nscenario is realized, and may take additional second-stage recourse actions\nafter a scenario is realized. The goal is typically to minimize the total\nexpected cost. A criticism of this model is that the underlying probability\ndistribution is itself often imprecise! To address this, a versatile approach\nthat has been proposed is the {\\em distributionally robust 2-stage model}:\ngiven a collection of probability distributions, our goal now is to minimize\nthe maximum expected total cost with respect to a distribution in this\ncollection.\n We provide a framework for designing approximation algorithms in such\nsettings when the collection is a ball around a central distribution and the\ncentral distribution is accessed {\\em only via a sampling black box}.\n We first show that one can utilize the {\\em sample average approximation}\n(SAA) method to reduce the problem to the case where the central distribution\nhas {\\em polynomial-size} support. We then show how to approximately solve a\nfractional relaxation of the SAA (i.e., polynomial-scenario\ncentral-distribution) problem. By complementing this via LP-rounding algorithms\nthat provide {\\em local} (i.e., per-scenario) approximation guarantees, we\nobtain the {\\em first} approximation algorithms for the distributionally robust\nversions of a variety of discrete-optimization problems including set cover,\nvertex cover, edge cover, facility location, and Steiner tree, with guarantees\nthat are, except for set cover, within $O(1)$-factors of the guarantees known\nfor the deterministic version of the problem.\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".