In this thesis, we study the intersection of optimization and machine learning, especially how to use machine learning and optimization tools to make decisions. In Chapter 1, we propose a novel approach for accurate policy evaluation in personalized pricing. We solve an optimization problem to evaluate new pricing strategies, while searching over some worst case revenue functions.
In Chapter 2, we consider problems where parameters are predicted using a machine learning model to be used for downstream optimization tasks. Recent works have proposed an integrated approach, accounting for how predictions are used in the downstream optimization problem, instead of just minimizing prediction error. We analyze the asymptotic performance of methods under the integrated and traditional approaches, in the sense of first-order stochastic. We argue that when the model class is rich enough to cover the ground truth, the traditional predict-then-optimize approach outperforms the integrated approach, and the performance ordering between the two approaches is reversed when the model is misspecified.
In Chapter 3, we present a new class of architectures for reinforcement learning, Implicit Two-Tower (ITT) policies, where the actions are chosen based on the attention scores of their learnable latent representations with those of the input states. We show that ITT-architectures are particularly suited for evolutionary optimization and the corresponding policy training algorithms outperform their vanilla unstructured implicit counterparts as well as commonly used explicit policies.
In Chapter 4, we consider an active learning problem, in which the learner has the ability to sequentially select unlabeled samples for labeling. A typical active learning algorithm would sample more points at “difficult" regions in the feature space to more efficiently use the sampling budget and reduce excess risk. For nonparametric classification with smooth regression functions, we show that nuances in notions of margin that involves the uniqueness of the Bayes classifier, having no apparent effect on rates in passive learning, determine whether or not any active learner can outperform passive learning rates.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/8c2g-x967 |
| Date | January 2023 |
| Creators | Zhao, Yunfan |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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