Robustness of Sequential Estimation in Revenue Management

We propose and analyze a sequential design of price experimentation that balances the learning and earning trade-off in revenue management. Assuming the demand function belongs to a parametric family with an unknown parameter value, we derive a closed-form stopping rule based on the realized revenue function and observed Fisher information. The decision maker adaptively stops learning and optimizes a price based on the cumulative information and there is no need to find an optimal "fixed" sample size a priori, which is infeasible with the lack of knowledge on the demand function. We show our proposed policy achieves an asymptotically optimal min-max regret when the initial price is exogenously given. That is, in the worst case scenario under which an adversary selects the parameter to make the retailer's regret the most in her choice of sample size for estimation, our proposed policy can effectively nullify the adversary's ill-intention and hence achieve a robust performance as the number of periods in the sales horizon increases. We further show that such a benefit in robustness does not persist under any fixed sample size experiments, highlighting the advantage of using sequential estimation over predetermined fixed-sample size procedure