Generalized Inverse Optimization through Online Learning
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Inverse optimization is a powerful paradigm for learning preferences and restrictions that explain the behavior of a decision maker, based on a set of external signal and the corresponding decision pairs. However, the majority of existing inverse optimization algorithms are designed specifically in batch setting, where all the data are available in advance. As a consequence, there has been rare use of these methods in an online setting that actually is more suitable for real-time applications. In this paper, we propose a general framework for inverse optimization through online learning. Specifically, we develop an online learning algorithm that uses an implicit update rule which can handle noisy data. Moreover, under additional regularity assumptions in terms of the data and the model, we prove that our algorithm converges at a rate of O(1/√(T)) and is statistically consistent. In our experiments, we show the online learning approach can learn the parameters with a great accuracy and is very robust to noises, and achieves a drastic improvement in computational efficacy over the batch learning approach.
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