Promotion Optimization Engine

AB InBev Global Analytics Hackathon: Team - Simpson's Paradox

This project implements a hierarchical regression model for promotion optimization, developed during the AB InBev Global Analytics Hackathon. The solution focuses on optimizing promotional spend allocation across a multi-level product hierarchy (brand, price segment, pack type, size, and SKU) while respecting business constraints. Our team placed 7th globally out of 150+ teams in the competition.

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Model Architecture

The model uses a hierarchical parameter structure where each parameter consists of two components:

1. A global parameter $w$ that represents the shared behavior across all SKUs
2. A hierarchical parameter $w^h$ that captures SKU-specific deviations from the global

This structure is implemented through the BaseModuleClass, which manages both global and hierarchical parameters. The ActivatedParameter class wraps PyTorch parameters with configurable activation functions (tanh, sigmoid, or relu).

We enforce the hierarchical structure through regularization (instead of KL divergence) to ensure SKU-level parameters stay close to the global distribution:

$$\mathcal{L}_{\text{reg}} = \lambda_h \sum_k (w_k^h)^2 + \lambda_r \sum_k w_k^2$$

where $\lambda_h$ penalizes SKU-level deviation and $\lambda_r$ is standard L2 regularization on global weights.

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Layers

Baseline: Predicts base sales from time trend and lagged sales with hierarchical seasonality effects per SKU

$$\hat{b} = \sigma(w_0) + \bigl(\tanh(w_1) + \tanh(w_1^h)\bigr) \alpha t + \bigl(\tanh(w_2) + \tanh(w_2^h)\bigr) y_{t-1}$$

Mixed Effect: Computes a macroeconomic scaling factor $m$ and an ROI multiplier $r$ that scales promotional uplift based on macro conditions

$$m = 1 + \tanh\left((\tanh(w_m) + \tanh(w_m^h))^\top x_{\text{macro}}\right)$$

$$r = 1 + \tanh\left((\tanh(w_r) + \tanh(w_r^h)) \cdot m\right)$$

Discount: Computes promotional uplift $u$ as a hierarchically-weighted linear function of discount spend $d$

$$u = \bigl(\sigma(w_d) + \sigma(w_d^h)\bigr) \cdot d$$

Volume Conversion: Converts sales predictions to volume using independent conversion parameters

$$v = \sigma(w_v) \hat{y} + \tanh(w_i)$$

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Final Prediction

The final sales prediction combines all components:

$$\hat{y} = \hat{b} \cdot \prod_j m_j + \sum_j u_j \cdot \prod_j r_j$$

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Optimization Engine

Given a trained model, the optimizer backpropagates through the frozen network to find the discount allocation $d^*$ that minimizes:

$$\mathcal{L}_{\text{opt}} = -\Delta_{\text{NR}} - \lambda_\rho \cdot \rho + \sum_c \lambda_c \mathcal{L}_c$$

where $\Delta_{\text{NR}}$ is the increase in net revenue over baseline, and $\rho$ is defined as:

$$\rho = \frac{\sum \hat{y}_{\text{opt}} - \sum \hat{y}_{\text{init}}}{\sum d + \epsilon}$$

Penalty terms $\mathcal{L}_c$ enforce the following constraints: brand-level discount caps, pack-type limits, price segment bounds, volume variation limits, and non-negativity of discounts.