Blind Network Revenue Management and Bandits with Knapsacks under Limited Switches

David Simchi-Levi, Yunzong Xu, Jinglong Zhao

Our work is motivated by a common business constraint in online markets. While firms respect the advantages of dynamic pricing and price experimentation, they must limit the number of price changes (i.e., switches) to be within some budget due to various practical reasons. We study both the classical price-based network revenue management problem in the distributionally-unknown setup, and the bandits with knapsacks problem. In these problems, a decision-maker (without prior knowledge of the environment) has finite initial inventory of multiple resources to allocate over a finite time horizon. Beyond the classical resource constraints, we introduce an additional switching constraint to these problems, which restricts the total number of times that the decision-maker makes switches between actions to be within a fixed switching budget. For such problems, we show matching upper and lower bounds on the optimal regret, and propose computationally-efficient limited-switch algorithms that achieve the optimal regret. Our work reveals a surprising result: the optimal regret rate is completely characterized by a piecewise-constant function of the switching budget, which further depends on the number of resource constraints -- to the best of our knowledge, this is the first time the number of resources constraints is shown to play a fundamental role in determining the statistical complexity of online learning problems. We conduct computational experiments to examine the performance of our algorithms on a numerical setup that is widely used in the literature. Compared with benchmark algorithms from the literature, our proposed algorithms achieve promising performance with clear advantages on the number of incurred switches. Practically, firms can benefit from our study and improve their learning and decision-making performance when they simultaneously face resource and switching constraints.

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