Title: Decision Making with Coupled Learning
Description: Operational decisions can be complicated by the presence of uncertainty. In many cases, there exist means to reduce uncertainty, though these may come at a cost. Decision makers then face the dilemma of acting based on current, incomplete information versus investing in trying to minimize uncertainty. Understanding the impact of this trade-off on decisions and performance is the central topic of this thesis. When attempting to construct probabilistic models based on data, operational decisions often affect the amount and quality of data that is collected. This introduces an exploration-exploitation trade-off between decisions and information collection. Much of the literature has sought to understand how operational decisions should be modified to incorporate this trade-off. While studying two well-known operational problems, we ask an even more basic question: does the exploration-exploitation trade-off matter in the first place? In the first two parts of this thesis we focus on this question in the context of the newsvendor problem and sequential auctions with incomplete private information.

We first analyze the well-studied stationary multi-period newsvendor problem, in which a retailer sells perishable items and unmet demand is lost and unobserved. This latter limitation, referred to as demand censoring, is what introduces the exploration-exploitation trade-off in this problem. We focus on two questions: i.) what is the value of accounting for the exploration-exploitation trade-off; and, ii.) what is the cost imposed by having access only to sales data as opposed to underlying demand samples? Quite remarkably, we show that, for a broad family of tractable cases, there is essentially no exploration-exploitation trade-off; i.e., there is almost no value of accounting for the impact of decisions on information collection. Moreover, we establish that losses due to demand censoring (as compared to having full access to demand samples) are limited, but these are of higher order than those due to ignoring the exploration-exploitation trade-off. In other words, efforts aimed at improving information collection concerning lost sales are more valuable than analytic or computational efforts to pin down the optimal policy in the presence of censoring.

In the second part of this thesis we examine the problem of an agent bidding on a sequence of repeated auctions for an item. The agent does not fully know his own valuation of the object and he can only collect information if he wins an auction. This coupling introduces the exploration-exploitation trade-off in this problem. We study the value of accounting for information collection on decisions and find that: i.) in general the exploration-exploitation trade-off cannot be ignored (that is, in some cases ignoring exploration can substantially affect rewards), but ii.) for a broad class of instances, ignoring exploration can indeed produce nearly optimal results. We characterize this class through a set of conditions on the problem primitives, and we demonstrate with examples that these are satisfied for common settings found in the literature. In the third part of this thesis we study the impact of uncertainty in the context of inventory record inaccuracies in inventory management systems.

Record inaccuracies, mismatches between physical and recorded inventory, are frequently encountered in practice and can markedly affect revenues. Most of the literature is devoted to analyzing the cost-benefit relationship between investing in means to reduce inaccuracies and accounting for them in operational decisions. We focus on the less explored approach of using available data to reduce the uncertainty in inventory. In practice, collecting Point Of Sale (POS) data is substantially simpler than collecting stock information. We propose a model in which inventory is regarded as a virtually unobservable quantity and POS data is used to infer its state over time. Additionally, our method also works as an effective estimator of censored demand in the presence of inaccurate records. We test our methodology with extensive numerical experiments based on both simulated and actual retailing data. The results show that it is remarkably effective in inferring unobservable past statistics and predicting future stock status, even in the presence of severe data misspecifications.