用市场模型精准分配任务与执行间的信用,避免误判进度
Attribution Markets: A Fisher-Market Formulation for Fractional Credit Assignment Between Planned Tasks and Performed Actions

- 将计划任务和实际动作建模为带预算的买家与可分割商品
- 提出带保留价和现金选项的机制,确保预算约束和无效数据过滤
- 引入熵正则化统一处理噪声敏感性,适合项目管理与归因分析场景
个人与组织的规划系统常存在计划(任务预算)与实际执行(动作时长与描述)记录脱节的问题。现有系统采用排他性全有或全无关联,导致相关但未链接的努力被忽略,且错误标记活跃目标为停滞。本文将该关联问题形式化为拟线性费雪市场:计划任务为预算受限的买家,实际动作为可分割商品,融合文本、结构与时间信号生成估值。引入卖方保留价与买方现金选项,理论证明预算守恒、硬预算上限及垃圾数据过滤。进一步引入凹形完成效用函数,随任务接近计划而递减进度价值;标准收敛理论不适用,通过满足对角占优条件的饱足阈值不动点解决,实证验证于随机与对抗实例。构建去循环多种子基准,揭示市场零熵均衡对亲和度噪声更敏感,优于熵正则化最优传输的稳定解。提出单参数熵正则化推广,结合自适应规则调节正则强度。报告完整可复现参数,坦诚讨论局限,并关联多触点归因、最优传输与在线费雪市场算法。
原文摘要 · Abstract (English)
Personal and organizational planning systems maintain two records that drift apart: what was planned (a task's effort budget) and what was done (a logged action's duration and description). Existing systems bridge them with an exclusive, all-or-nothing link that strands genuinely related but unlinked effort and reports false stalls on active goals. We formulate the bridge as a quasi-linear Fisher market: planned tasks are budget-constrained buyers, performed actions are divisible goods, and a fused text/structural/temporal signal sets each buyer's valuation. Two market instruments - a seller reserve price and a buyer cash option - yield conservation, a hard budget cap, and a provable junk filter as theorems. We extend the market with a concave completion utility discounting progress as a task nears its plan; standard convergence theory for the market's algorithm does not transfer here, resolved by a satiation-threshold fixed point with existence (Brouwer) and local uniqueness under an explicit diagonal-dominance condition, validated empirically on random and adversarial instances. A de-circularized, multi-seed benchmark - observed affinity corrupted independently of the scored ground truth - surfaces a genuine weak spot: the market's sharp, zero-entropy equilibrium is more sensitive to affinity noise than entropy-regularized optimal transport's permanently smoothed one. We resolve this with a one-parameter entropy-regularized generalization unifying the two, plus a noise-adaptive rule for its regularization strength. We report full reproducibility parameters, discuss limitations candidly, and relate the result to multi-touch attribution, optimal transport, and online Fisher-market algorithms.
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