| Summary: | In Chapters 2 and 3, given a finite number of populations, henceforth referred to as systems, we are concerned with the problem of dynamically learning the statistical characteristics of the systems to ultimately select the best system. This is an instance of ordinal optimization where probability distributions governing each system's performance are not known, but can be learned via sequential sampling.
In Chapter 2 we study the classical setting where the ultimate goal is to choose the system with the highest mean, while in Chatper 3 the systems are compared based on quantiles. The latter setting is appropriate when downside or upside risk is more crucial than the mean performance. In both settings, we use large deviations theory to derive key structural insights on near-optimal allocation of the sampling budget, which are leveraged to design dynamic sampling policies that are practically implementable. We rigorously provide (asymptotic) performance guarantees for these policies. Further, we show via numerical testing that the proposed (nonparametric) policies perform competitively compared to other benchmark policies.
In Chapter 4, we investigate how the presence of product reviews affects a dynamic-pricing monopolist. A salient feature of our problem is that the demand function evolves over time in conjunction with the dynamics of the review system. The monopolist strives to maximize its total expected revenue over a finite horizon by adjusting prices in response to the review dynamics. To formulate the problem in tractable form, we study a fluid model, which is a good approximation when the volume of sales is large. This formulation lends itself to key structural insights, which are leveraged to design a well-performing pricing policy for the underlying revenue maximization problem. The proposed policy allows a closed-form expression for price and its performance is asymptotically near-optimal. We show via simulation and counterfactual analysis the effectiveness of the proposed policy in online markets with product reviews.
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