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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2603.08087 |
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| _version_ | 1866918379891195904 |
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| author | Peyrousset, Nils Tran, Benoît |
| author_facet | Peyrousset, Nils Tran, Benoît |
| contents | Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of metrics, this duality no longer yields Fortet-Mourier bounds. This paper develops a direct stability approach using the primal optimal transport formulation. We prove that under minimal regularity conditions and a regret domination property, the optimal value function remains Lipschitz continuous with respect to problem-dependent transport costs. Our approach works directly with transport couplings rather than relying on dual representations to establish stability bounds. We present two applications: (1) For linear programs with continuous second-stage, we show that regret domination holds with constants depending on dual bounds and Lipschitz properties, using sensitivity analysis. (2) For mixed-integer second-stage problems, we show that combinatorial structure can be exploited to obtain tight regret bounds. We analyze several examples as illustrations. These results provide theoretical justification for problem-dependent scenario reduction approaches and enable their application to both continuous and discrete stochastic programs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability of Two-Stage Stochastic Programs Under Problem-Dependent Costs Peyrousset, Nils Tran, Benoît Optimization and Control Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of metrics, this duality no longer yields Fortet-Mourier bounds. This paper develops a direct stability approach using the primal optimal transport formulation. We prove that under minimal regularity conditions and a regret domination property, the optimal value function remains Lipschitz continuous with respect to problem-dependent transport costs. Our approach works directly with transport couplings rather than relying on dual representations to establish stability bounds. We present two applications: (1) For linear programs with continuous second-stage, we show that regret domination holds with constants depending on dual bounds and Lipschitz properties, using sensitivity analysis. (2) For mixed-integer second-stage problems, we show that combinatorial structure can be exploited to obtain tight regret bounds. We analyze several examples as illustrations. These results provide theoretical justification for problem-dependent scenario reduction approaches and enable their application to both continuous and discrete stochastic programs. |
| title | Stability of Two-Stage Stochastic Programs Under Problem-Dependent Costs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.08087 |