Paper: arXiv 2604.25977

Authors: Nilavra Pathak, Olivier Jeunen, Eric Lambert

Abstract

Organizations routinely make strategic budget allocations under operational constraints, but often lack a principled way to assess whether realized allocations were close to the best feasible choices in hindsight. We present a retrospective auditing framework based on hindsight regret, defined as the opportunity cost of the realized allocation relative to a constraint-faithful benchmark under the same budget and stability guardrails. The framework estimates regime-specific spend–response functions from historical logs, computes feasible hindsight allocations via constrained optimization, and propagates uncertainty through Monte Carlo evaluation to produce regret distributions, expected lift, and probability-of-improvement summaries. This separates allocation inefficiency from uncertainty in the estimated response surfaces. Experiments on real marketing allocation logs show that the framework yields interpretable post-hoc diagnostics and reveals a practical trade-off between allocation flexibility and detectability: moderate feasible reallocations often capture most measurable gain, while larger shifts move into weak-support regions with higher uncertainty. The result is a practical method for auditing historical budget decisions when online experimentation is costly or infeasible.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines formal structural causal modeling and uncertainty quantification with a practical implementation strategy for analyzing real-world marketing log data. By integrating constrained optimization and Monte Carlo simulation with empirical performance benchmarks, it bridges the gap between advanced theoretical decision-making and operational backtesting needs.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Audit Marketing Budget Inefficiency] --> B[<b>Data:</b> Historical Logs & Constraints]
    B --> C[<b>Modeling:</b> Estimate Spend-Response Surfaces]
    C --> D[<b>Optimization:</b> Feasible Hindsight Allocation]
    D --> E[<b>Analysis:</b> Monte Carlo Uncertainty Propagation]
    E --> F[<b>Outcomes:</b> Regret Distributions & Lift Summaries]
    F --> G[<b>Key Finding:</b> Trade-off between flexibility & detectability]

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0 of 75 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.