🤖 AI Summary
This paper studies a multi-stage dynamic pricing problem in retail settings where demand distributions are unknown, price adjustments are restricted to discrete time points, and each adjustment affects a batch of arriving customers—posing challenges including model ambiguity, unknown arrival processes, and batch-wise demand impact. To address these, we propose an Adaptive Robust Learning (ARL) strategy: it dynamically constructs a “probabilistically credible” demand ambiguity set from sales data and integrates stochastic optimization with Bayesian updating to jointly optimize robustness and learning efficiency. We derive a theoretical regret upper bound that explicitly depends on the customer arrival pattern. Experiments demonstrate that ARL significantly outperforms baseline methods—including distributionally robust optimization, Follow-the-Leader, and UCB—in both expected revenue and Value-at-Risk (VaR), effectively bridging the gap between strong robustness and low regret.
📝 Abstract
We study dynamic pricing over a finite number of periods in the presence of demand model ambiguity. Departing from the typical no-regret learning environment, where price changes are allowed at any time, pricing decisions are made at pre-specified points in time and each price can be applied to a large number of arrivals. In this environment, which arises in retailing, a pricing decision based on an incorrect demand model can significantly impact cumulative revenue. We develop an adaptively-robust-learning (ARL) pricing policy that learns the true model parameters from the data while actively managing demand model ambiguity. It optimizes an objective that is robust with respect to a self-adapting set of demand models, where a given model is included in this set only if the sales data revealed from prior pricing decisions makes it ``probable''. As a result, it gracefully transitions from being robust when demand model ambiguity is high to minimizing regret when this ambiguity diminishes upon receiving more data. We characterize the stochastic behavior of ARL's self-adapting ambiguity sets and derive a regret bound that highlights the link between the scale of revenue loss and the customer arrival pattern. We also show that ARL, by being conscious of both model ambiguity and revenue, bridges the gap between a distributionally robust policy and a follow-the-leader policy, which focus on model ambiguity and revenue, respectively. We numerically find that the ARL policy, or its extension thereof, exhibits superior performance compared to distributionally robust, follow-the-leader, and upper-confidence-bound policies in terms of expected revenue and/or value at risk.
