We study how to construct compressed datasets that suffice to recover optimal decisions in linear programs with unknown cost vector $c$ lying in a prior set $\mathcal{C}$. Recent work by Bennouna et al. (2025a) provides an exact geometric characterization of sufficient decision datasets (SDDs) via an intrinsic decision-relevant dimension $d^\star$. However, their algorithm for constructing minimum-size SDDs requires solving mixed-integer programs. In this paper, we establish hardness results: computing $d^\star$ is NP-hard and deciding whether a dataset is globally sufficient is coNP-hard, thereby resolving the open problem posed by Bennouna et al. (2026). To circumvent worst-case intractability, we introduce pointwise sufficiency, a relaxation that requires sufficiency for an individual cost vector. We provide a polynomial-time cutting-plane algorithm to construct pointwise-sufficient decision datasets under nondegeneracy. In a data-driven regime with i.i.d. costs, we propose a cumulative algorithm that aggregates decision-relevant directions across samples, yielding a stable compression scheme of size at most $d^\star$. This leads to a distribution-free PAC guarantee: with high probability over the training sample, the pointwise sufficiency failure probability on a fresh draw is at most $\tilde{O}(d^\star/n)$, and this rate is tight up to logarithmic factors. Finally, we apply decision-sufficient representations to contextual linear optimization, obtaining compressed predictors with generalization bounds scaling as $\tilde{O}(\sqrt{d^\star/n})$ rather than $\tilde{O}(\sqrt{d/n})$, where $d$ is the ambient cost dimension.

We propose an online adaptive sampling algorithm for solving stochastic nonsmooth difference-of-convex (DC) problems under time-varying distributions. At each iteration, the algorithm relies solely on data generated from the current distribution and employs distinct adaptive sampling rates for the convex and concave components of the DC function, a novel design guided by our theoretical analysis. We show that, under proper conditions on the convergence of distributions, the algorithm converges subsequentially to DC critical points almost surely. Furthermore, the sample size requirement of our proposed algorithm matches the results achieved in the smooth case or when a measurable subgradient selector is available, both under static distributions. A key element of this analysis is the derivation of a novel $O(\sqrt{p/n})$ pointwise convergence rate (modulo logarithmic factors) for the sample average approximation of subdifferential mappings, where $p$ is the dimension of the variable and $n$ is the sample size – a result of independent interest. Numerical experiments confirm that the proposed algorithm is both efficient and effective for addressing stochastic nonsmooth problems.

Although generative AI has been applied to protect wildlife in various scenarios, studies have identified the lack of an integrated application toolkit to curb illegal wildlife trade. We therefore introduce DRCO1, the first application framework that is integrated with LLM by proposing useful policies. In the Decision-Making Module, a black-box LLM, combined with a refined ReAct-like prompting template, selects policy promoters in one region. In the Restrictive-Partial-Legalization Module, our innovative Dynamic Iterative Constraint Method is employed to calculate the controlled volume of wildlife trade under the influence of policy, which may provide an idea for Explainable AI research. The Curve-fitting module fits current and future data into a curve with an 86.27% fit to the original Product Life Cycle Curve. The Optimal-Algorithm Module proposes a Dynamic WP-CUCB Algorithm with Policy Consideration to optimize the allocation of wildlife patrol resources in the region. Experiments indicate that policies generated by DRCO can lead to significant control and promote "AI for social good". Our code and more details will be open-sourced online.