Solving contextual chance-constrained programming under decision-dependent uncertainty
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908819026608128 |
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| author | Liu, Xiangting Wang, Shengran Yan, Kaile Zhang, Zhi-Hai |
| author_facet | Liu, Xiangting Wang, Shengran Yan, Kaile Zhang, Zhi-Hai |
| contents | We study contextual chance-constrained programming under decision-dependent uncertainty. In this setting, a decision not only needs to satisfy constraints but also alters the distribution of uncertain outcomes. This dependency makes the problem particularly difficult: because feasibility probabilities vary with decisions, it creates both statistical endogeneity and computational intractability. To address this, we propose a nonparametric approximation method based on Contextual Cluster Weights (CCW). For any given decision and context, CCW constructs a local neighborhood (cluster) of ``similar" historical observations and assigns them equal weight. This approach successfully renders both the objective and chance constraints tractable, while providing uniform-in-decision consistency guarantees. Furthermore, we develop reformulations that use pre-calculated clusters. We show that under a specific nestedness condition, these reformulations yield a convex feasible region, which allows for efficient solving. Experiments, including a case study with JD.com, demonstrate that our method outperforms benchmarks in solution quality, feasibility reliability, and runtime. This framework offers a scalable and data-driven approach for firms to make reliable operational decisions when their actions influence uncertainty. It effectively balances performance, risk, and robustness, while remaining interpretable and implementable in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving contextual chance-constrained programming under decision-dependent uncertainty Liu, Xiangting Wang, Shengran Yan, Kaile Zhang, Zhi-Hai Optimization and Control We study contextual chance-constrained programming under decision-dependent uncertainty. In this setting, a decision not only needs to satisfy constraints but also alters the distribution of uncertain outcomes. This dependency makes the problem particularly difficult: because feasibility probabilities vary with decisions, it creates both statistical endogeneity and computational intractability. To address this, we propose a nonparametric approximation method based on Contextual Cluster Weights (CCW). For any given decision and context, CCW constructs a local neighborhood (cluster) of ``similar" historical observations and assigns them equal weight. This approach successfully renders both the objective and chance constraints tractable, while providing uniform-in-decision consistency guarantees. Furthermore, we develop reformulations that use pre-calculated clusters. We show that under a specific nestedness condition, these reformulations yield a convex feasible region, which allows for efficient solving. Experiments, including a case study with JD.com, demonstrate that our method outperforms benchmarks in solution quality, feasibility reliability, and runtime. This framework offers a scalable and data-driven approach for firms to make reliable operational decisions when their actions influence uncertainty. It effectively balances performance, risk, and robustness, while remaining interpretable and implementable in practice. |
| title | Solving contextual chance-constrained programming under decision-dependent uncertainty |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.07286 |