Customized objective function for budget optimization.

[Aminshnn]

I have a marketing mix modeling setup with different outcome categories, which I index as
(c = 1,2,\dots,C).

I also have a vector of spending variables (x) that includes spending across all categories (for example, media spend variables across different channels and categories).

For each category (c), I train a separate model of the form:

[
y_c = f_c(x)
]

where:

• (y_c) is the outcome for category (c),
• (x) is the vector of all spending variables including spending variables of all categories.

Importantly, when training the model for category (c), I do not exclude spending variables from other categories. In other words, every model (f_c(\cdot)) uses the full spending vector (x) as input.

After training these models, I would like to perform budget optimization. However, instead of optimizing each category model separately, I would like to optimize a combined objective function of the form:

[
\max_x \sum_{c=1}^{C} w_c , y_c
]

where:

• (w_c) is a weight assigned to the outcome from category (c),
• (y_c = f_c(x)).

The goal is therefore to determine the optimal spending vector (x) that maximizes the weighted sum of outcomes across all categories.

I am wondering if it is possible to do it in Google Meridian. or I should reconstruct functions and optimize the budget manually. If I need to reconstruct the functions, how can I do that?

One more question. Does Google Meridian optimizes the budget based on the KPI or ROI? Suppose KPI is acquisition and we have revenue_per_kpi.

Thanks

[cpulavarthi]

Hello @Aminshnn,

Thank you for contacting us!

For your first question about optimizing budget over multiple models that use the same media as predictors, currently Meridian does not support joint budget optimization across multiple separately trained models for different outcome categories. You would need to tailor the functions and optimization process to meet your needs.

For your 2nd question, when revenue_per_kpi is provided, Meridian optimizes the budget based on ROI (maximizing total incremental revenue). If you have revenue_per_kpi, Meridian will automatically convert your acquisition KPI into a monetary value to calculate ROI as incremental revenue divided by spend. By default, the BudgetOptimizer will find the optimal allocation to maximize this overall ROI for a fixed budget. If revenue_per_kpi was unknown, the optimizer would default to maximizing the incremental KPI (acquisitions) instead. If you want to optimize towards a target ROI or marginal ROI (mROI) instead of a fixed budget, you can set fixed_budget=False and pass a target_roi or target_mroi.

Feel free to reach out if you have any further questions regarding this.

Google Meridian Support Team