Optimized allocation lower than initial allocation

[bhauryal-eliya]

Hello everyone,

I am using BudgetOptimizer from pymc_marketing.mmm.budget_optimizer to find the optimal allocation of marketing spend, and sometimes I get an allocation strategy from the solver that results in the optimized allocation being less than the initial allocation. Additionally, I noticed that when I increase budget constraints on channels, the optimized allocation drops even further than the initial allocation. I don't understand what could be happening; it would be great if someone could point out what is happening. Please let me know if I should share more details. Thanks in advance.

num_periods = X_test.shape[0]

# Total budget for the test set per channel
all_budget_per_channel = X_test[channels].sum(axis=0)

# Total budget for the test set
all_budget = all_budget_per_channel.sum()

# Weekly budget for each channel
weekly_budget = all_budget / num_periods

percentage_change = 0.5

mean_spend_per_period_test = (
    X_test[channels].mean()
)

budget_bounds = {
    key: [(1 - percentage_change) * value, (1 + percentage_change) * value]
    for key, value in (mean_spend_per_period_test).to_dict().items()
}

import pytensor.tensor as pt
from pymc_marketing.mmm.utility import _check_samples_dimensionality

def average_response(
    samples: pt.TensorVariable, budgets: pt.TensorVariable
) -> pt.TensorVariable:
    """Compute the average response of the posterior predictive distribution."""
    return pt.mean(_check_samples_dimensionality(samples)) * 1e5 # Random multiplier to increase response, avoid the derivative to be so small.


allocation, result = mmm.optimize_budget(
    budget=weekly_budget,
    budget_bounds=budget_bounds,
    num_periods=num_periods,
    utility_function=average_response,
)

sample_allocation = mmm.sample_response_distribution(
    allocation_strategy=allocation,
    time_granularity="weekly",
    num_periods=num_periods,
    noise_level=0.05,
)

baseline_allocation = (
    X_test[channels].mean()
).to_dict()

response_initial = mmm.sample_response_distribution(
    allocation_strategy=baseline_allocation,
    time_granularity="weekly",
    num_periods=num_periods,
    noise_level=0.05,
)

response_initial_contribution_original_scale = apply_sklearn_transformer_across_dim(
    data=response_initial["channel_contribution"]
    .unstack()
    .sum(dim="channel")
    .transpose(..., "date"),
    func=mmm.get_target_transformer().inverse_transform,
    dim_name="date",
)

response_optimized_contribution_original_scale = apply_sklearn_transformer_across_dim(
    data=sample_allocation["channel_contribution"]
    .unstack()
    .sum(dim="channel")
    .transpose(..., "date"),
    func=mmm.get_target_transformer().inverse_transform,
    dim_name="date",
)

PS: I have been trying to move to multi-dim API as well for budget allocation and currently facing an issue of not being able to replicate the results for single-geo, I plan to post it as a separate question.

[juanitorduz]

@carlosagostini do you have any hints here :) ?