Retailers often fear that trying new product mixes costs too much or is logistically difficult. The new study shows that even offering one carefully designed set of products to just one customer can sharply lower the worst‑case loss in revenue when no other data are available. The authors work with the multinomial logit model, assuming product revenues are known but customers’ preference weights are not.

In the one‑observation case the authors derive the exact optimal experiment. They identify a triple (k★, p★, ℓ★) and prescribe the following policy: run the experiment with the revenue‑prefix assortment [k★]. If that customer buys, commit to the final assortment [p★]; if the customer makes no purchase, switch to the final assortment [ℓ★] This rule minimises the maximum possible regret against any unknown preference vector.

When no experimentation is possible, the best any retailer can do is choose a revenue‑prefix assortment [k] that minimises the two worst losses: the loss from excluding a high‑revenue product, r{k+1}, and the loss from inviting a low‑revenue product, r1 – rk. The minimum of these two terms equals the minimax regret for zero experiments.

The authors also investigate the limit of learning from a single type of experiment. Even if a retailer can observe an infinite number of customers exposed to the same experimental assortment, the worst‑case regret will never drop to zero unless the retailer uses at least n – 1 distinct experimental assortments. In other words, a single fixed experiment provides coverage for only a limited portion of the product line.

These results clarify exactly when a single experiment is worth the effort and when retailers must design richer experimental programmes to eliminate regret.