ROI Maximization in Stochastic Online Decision-Making
This addresses a specific challenge for companies needing efficient decision-making on innovation proposals, though it is incremental as it builds on existing online learning frameworks.
The paper tackles the problem of maximizing Return on Investment (ROI) in online decision-making for companies evaluating technological innovations, by introducing an algorithm that provably converges to an optimal policy at a rate of order min{1/(NΔ^2), N^{-1/3}}.
We introduce a novel theoretical framework for Return On Investment (ROI) maximization in repeated decision-making. Our setting is motivated by the use case of companies that regularly receive proposals for technological innovations and want to quickly decide whether they are worth implementing. We design an algorithm for learning ROI-maximizing decision-making policies over a sequence of innovation proposals. Our algorithm provably converges to an optimal policy in class $Π$ at a rate of order $\min\big\{1/(NΔ^2),N^{-1/3}\}$, where $N$ is the number of innovations and $Δ$ is the suboptimality gap in $Π$. A significant hurdle of our formulation, which sets it aside from other online learning problems such as bandits, is that running a policy does not provide an unbiased estimate of its performance.