Optimising Non-Linear Treatment Effects in Pricing and Promotions
What is this series of articles about?
Welcome to my series on Causal AI, where we will explore the integration of causal reasoning into machine learning models. Expect to explore a number of practical applications across different business contexts.
In the last article we covered using Double Machine Learning and Linear Programming to optimise treatment strategies. This time we will continue with the theme of optimisation exploring optimising non-linear treatment effects in Pricing & Promotions.
If you missed the last article on Double Machine Learning and Linear Programming, check it out here:
Using Double Machine Learning and Linear Programming to optimise treatment strategies
Introduction
This article will showcase how we can optimise non-linear treatment effects in pricing (but the ideas can also be applied across marketing and other domains too).
In this article I will help you understand:
- Why is it common to have non-linear treatment effects in pricing?
- What tools from our Causal AI toolbox are suitable for estimating non-linear treatment effects?
- How can non-linear programming be used to optimise pricing?
- A worked case study in Python working through how we can combine our Causal AI toolbox and non-linear programming to optimise pricing budgets.
The full notebook can be found here:
causal_ai/notebooks/using dml and lp to optimise treatment strategies.ipynb at main ·…
Why is it common to have non-linear treatment effects in pricing?
Diminishing returns
Let's take the example of a retailer adjusting the price of a product. Initially lowering the price might lead to a significant increase in sales. However, as they continue to lower the price, the increase in sales may start to plateau. We call this diminishing returns. As illustrated below, the effect of diminishing returns is generally non-linear.
Diminishing returns can be observed across various fields beyond pricing. Some common examples are:
- Marketing – Increasing social media spend can increase customer acquisition, but as time goes on it becomes more difficult to target new, untapped audiences.
- Farming – Adding fertilizer to a field can increase crop yield significantly initially, but this effect will very quickly start to diminish.
- Manufacturing – Adding more workers to a production process will improve efficiencies, but each additional worker may contribute less to the overall output.
This makes me start to wonder, if diminishing returns are so common, then which techniques from our Causal AI toolbox are capable of handling this?
What methods from our Causal AI toolbox are suitable for estimating non-linear treatment effects?
Toolbox
There are two key questions which we will ask to help us identify what methods from our Causal AI toolbox are suitable for our Pricing problem:
- Can it handle continuous treatments?
- Can it capture non-linear treatment effects?
Below we can see a summary of how suitable each method is:
- Propensity score matching (PSM) – Treatment needs to be binary ❌
- Inverse-propensity score matching (IPSM) – Treatment needs to be binary ❌
- T-Learner – Treatment needs to be binary ❌
- Double Machine Learning (DML) – Treatment effect is linear ❌
- Doubly-Robust Learner (DR) – Treatment needs to be binary ❌
- S-Learner – Can handle continuous treatments and non-linear relationships between the treatment and outcome if an appropriate machine learning algorithm (e.g. gradient boosting) is used
