Non-Linear Counterfactual Aggregate Optimization
This work addresses optimization challenges in scenarios like A/B testing where non-linear success criteria are more relevant than expected payoffs, though it appears incremental as it builds on concentration properties of sums.
The paper tackles the problem of optimizing non-linear functions of aggregated outcomes (like sums of many small contributions) by developing a scalable descent algorithm that directly targets the objective rather than maximizing individual expectations. This approach enables applications such as maximizing the probability of successful A/B tests by focusing on exceeding specific uplift thresholds.
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the maximization of the expectation of the individual contribution. By leveraging the concentration properties of the sum of individual outcomes, we derive a scalable descent algorithm that directly optimizes for our stated objective. This allows for instance to maximize the probability of successful A/B test, for which it can be wiser to target a success criterion, such as exceeding a given uplift, rather than chasing the highest expected payoff.