Decision-Making Under Complete Uncertainty: You Will Not Regret Being Greedy
Provides theoretical guarantees for greedy decision-making under Knightian uncertainty, relevant to decision theorists and practitioners in high-stakes domains.
The paper studies worst-case regret of the greedy strategy under complete uncertainty, proving it is rate-optimal with matching bounds and that regret vanishes as observations increase. Empirical tests on Google reviews align with theory.
In this paper, we propose a game-theoretic model to study the properties of the worst-case regret of the greedy strategy under complete (Knightian) uncertainty. In a game between a decision-maker (DM) and an adversarial agent (Nature), Nature chooses an unknown state determining the distribution of ratings for each product. The DM observes a realization of product ratings and then chooses a product according to a strategy. For arbitrary numbers of products and ratings, we first study the equal-observations case in which every product has the same number of observations. In this benchmark, we establish matching upper and lower bounds on the worst-case regret, showing that the regret vanishes as the number of observations increases and that the greedy strategy is rate-optimal up to universal constants. In the special case with two products and two ratings, we show that with one observation per product the greedy strategy is minimax-optimal with respect to worst-case regret. We then allow products to have different numbers of observations. Greedy remains robust in a conservative sense: its worst-case regret is controlled by the least-reviewed product. However, unequal numbers of observations can also change greedy's exact worst-case behavior. In particular, adding observations for only one product can increase greedy's worst-case regret. Finally, we test the model on data collected from Google reviews for restaurants, showing that the greedy strategy's empirical performance closely aligns with the theoretical findings.