We propose a novel procedure for correcting for the effects of sampling and parameter uncertainty in data-driven convex optimization. We consider the data-driven setting wherein the distribution lies in a parametric family with unknown parameter. The decision-maker possesses a historical data set, from which solves a prescriptive solution as a function mapping such a data set to decisions, and measures its out-of-sample performance as an average over data sets of the same size under the sampling distribution. As the parameter is unknown to the decision-maker, we argue that this problem is ill-defined and further prove that there cannot exist solutions generalizably optimal over all parameters. As such, we formulate the problem as a weighted multi-criteria optimization with weights defined by a density (termed ‘prior’) over the uncertain parameter, and call its optimal solution prior optimal. We prove that sufficient conditions for prior optimality reduces to functions of the sufficient statistic of the parametric family, and this function can be solved as a point-wise optima of a corrected function of the original objective, with terms accounting for parameter uncertainty and sampling uncertainty respectively. The correction for sampling interpretation is verified by a close to (but not) zero ex-ante regret against a perfect information oracle in numerical illustrations on the newsvendor and portfolio optimization problems.
Learning When Demand Is Unknown Airlines launching new routes cannot wait for years of historical data before deciding how many seats to offer at each fare or what prices to charge. They must learn when operating, often from incomplete feedback: selling 30 economy plus seats does not reveal whether demand was 30, 40, or more. In the accepted Operations Research paper “Semibandit Learning for Monotone Stochastic Optimization,” Rohan Ghuge, Zhengjia Zhuo, Arpit Agarwal, and Viswanath Nagarajan develop a general framework for such decisions. They identify a basic property, monotonicity, that allows an optimization method built for known demand distributions to become a learning algorithm for unknown distributions. The framework applies to airline and hotel revenue management, sequential posted pricing, and optimal-stopping problems. Even with partial, censored, or yes-or-no feedback, its cumulative performance gap grows essentially at the square root rate, best possible up to logarithmic factors. Firms can, therefore, improve decisions as data arrive without pausing operations for a separate data-gathering phase.
We present analytical and empirical arguments that competition over a nearly homogeneous service forces operators to oversupply scooters in urban centers. First, using deployment and ride data from operator APIs and city transportation departments, as well as telemetry data from one of the top three U.S. operators, we estimate average daily scooter utilization across nine major U.S. cities at 3.9%—half the 7.7% minimum utilization target set by transportation departments. Second, using a parsimonious game-theoretic model, we argue that if riders choose among available scooters roughly at random (e.g., the closest one), then in equilibrium all operators need to inflate their fleet sizes to preserve their market shares. Third, using granular data on riders’ choice sets and choices from Kansas City, MO, we provide evidence that these choices are indeed roughly random. Fourth, using our structurally estimated game-theoretic model, we find that in Kansas City, MO: (i) there is a 406% oversupply of scooters, (ii) the interaction between rider choice and competition accounts for 81% of this oversupply, and (iii) if the transportation department issued one more operator permit, oversupply would increase by an additional 82 pp. We conclude that transportation departments should be frugal with the number of permits they issue, and should welcome the consolidation of the scooter market.
We consider the generation of cuts in stochastic dual dynamic programming (SDDP) for multistage stochastic linear programming problems with stagewise dependent uncertainty in the right-hand side described by a nonlinear autoregressive process. We first derive cut formulas for the general nonlinear autoregressive process. For these general cuts, the computational tractability becomes a major challenge for SDDP-type algorithms. We are, however, able to develop tractable closed-form cut formulas for the special case of log-linear autoregressive processes. The obtained cuts are in general non-convex in the history of the stochastic process, but still linear in all decision variables, and thus can be directly incorporated into the subproblems in SDDP without compromising their linearity. If solvers do not allow for this, our formulas can be used to adapt the intercept of a given cut to a scenario at hand in a computationally tractable way. In this sense, cuts generated for one specific scenario are shared with other scenarios. Our findings are supported by a computational study of a hydrothermal scheduling problem, which demonstrates a favorable performance of our proposed version of SDDP compared to approaches from the literature.
When Sharing the Same Information Is Optimal Should a school advisor tailor recommendation letters to different employers or share the same information with everyone? Similar questions arise in start-up fundraising and biotech partnerships. In “Optimality of Public Persuasion for Single-Good Allocation,” Chen and Qi study how a sender can strategically disclose information when allocating an indivisible good to at most one self-interested receiver. The sender may send tailored private messages to individual receivers or publicly broadcast the same information to everyone. Surprisingly, the authors show that, when the sender has a known preference ordering over receivers, public persuasion is optimal even if receivers can subsequently communicate and share information. The optimal public mechanism can be derived from a simpler first-best allocation problem subject only to receivers’ participation constraints. The authors also develop a dual approach to characterize the structure of optimal mechanisms when the good’s characteristics are captured by a one-dimensional variable and all receivers’ utility functions are linear in this variable and reveal an intriguing decoupling structure.
