YUKTI: From Natural-Language Situations to Robust, Verifiable Decisions

YUKTI：从自然语言情境到稳健、可验证的决策

An Uncertainty-Typed Proposition IR, Assumption-Robust Pareto Frontiers, and a Regret Certificate 一种不确定性类型命题中间表示（IR）、假设稳健帕累托前沿及遗憾证明

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Abstract: Language models turn a worded situation into a numeric plan, and the dominant pipelines (NL4Opt, OptiMUS, ORLM, OR-LLM-Agent) commit to a single objective and point-valued coefficients, then solve once. For decisions that allocate real budget, effort, or clinical attention, that confidence is the failure mode: every objectified number is an assumption, and a plan optimal only if the guesses are exactly right is fragile — mimicry of computation.

摘要： 语言模型将文字描述的情境转化为数值化方案，而目前主流的流程（如 NL4Opt、OptiMUS、ORLM、OR-LLM-Agent）通常锁定单一目标和点值系数，然后进行一次性求解。对于涉及分配实际预算、人力或临床关注的决策而言，这种过度自信正是故障模式的根源：每一个客观化的数字本质上都是一种假设，如果一个方案仅在猜测完全准确时才最优，那么它就是脆弱的——这仅仅是对计算的模仿。

YUKTI changes the target of autoformulation. Its representation is a typed-proposition graph whose relationships carry shape priors, coefficient uncertainty, and provenance. YUKTI routes each stage to an exact, nonlinear, or evolutionary solver; couples stages by a distributional Pareto hand-off; and introduces Assumption-Robust Pareto Frontiers (ARPF), resampling assumptions (including structural epsilon-contamination) to score how often each action survives (rho).

YUKTI 改变了自动建模的目标。其表示形式是一个类型化的命题图，其中的关系携带了形状先验、系数不确定性和来源信息。YUKTI 将每个阶段路由至精确求解器、非线性求解器或进化求解器；通过分布式的帕累托交接（Pareto hand-off）耦合各阶段；并引入了“假设稳健帕累托前沿”（ARPF），通过重采样假设（包括结构性 epsilon 污染）来评估每个行动的存活频率（rho）。

We prove a bound making rho an exact factor of decision regret, add auditable traceability, and synthesize a benchmark-faithful data foundation when none exists (SRJANA). We validate three ways: under controlled misspecification the robust compromise cuts mean and tail regret by over 90% versus a naive point plan; on a regulated commercial decision we optimize inside a lawful action space and price the downside in euros; and on a real public dataset of 41,188 decisions an out-of-sample backtest beats the logged status quo by 34% and a naive point rule by 4% while reducing the optimizer’s curse.

我们证明了一个界限，使 rho 成为决策遗憾（regret）的精确因子，增加了可审计的追溯性，并在缺乏基准数据时合成了一个忠实于基准的数据基础（SRJANA）。我们通过三种方式进行了验证：在受控的错误设定下，稳健折中方案相比朴素的点值方案，将平均遗憾和尾部遗憾降低了 90% 以上；在受监管的商业决策中，我们在合法的行动空间内进行优化，并以欧元计价下行风险；在包含 41,188 项决策的真实公共数据集上，样本外回测显示其表现比记录的现状提升了 34%，比朴素的点值规则提升了 4%，同时减轻了“优化器诅咒”（optimizer’s curse）。

The solvers are standard; we claim no benchmark-SOTA win. A head-to-head shows an LLM given the correct numbers, and single-objective optimization, both incur about 47x the held-out regret of YUKTI — an LLM is a formulator, not a solver. Under long-range causal coupling, the forward hand-off becomes unsound, locating where it must become a backward-induction causal policy.

所使用的求解器均为标准工具；我们并不声称在基准测试中取得了 SOTA（最佳性能）。对比测试显示，即使给 LLM 提供正确的数字，或者使用单目标优化，其产生的留出集遗憾（held-out regret）约为 YUKTI 的 47 倍——LLM 是建模者，而非求解器。在长程因果耦合下，前向交接变得不可靠，这指出了必须转向后向归纳因果策略的场景。