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Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond
Haoxiang Wang · Bo Li · Han Zhao

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #1123
The vast majority of existing algorithms for unsupervised domain adaptation (UDA) focus on adapting from a labeled source domain to an unlabeled target domain directly in a one-off way. Gradual domain adaptation (GDA), on the other hand, assumes a path of $(T-1)$ unlabeled intermediate domains bridging the source and target, and aims to provide better generalization in the target domain by leveraging the intermediate ones. Under certain assumptions, Kumar et al. (2020) proposed a simple algorithm, Gradual Self-Training, along with a generalization bound in the order of $e^{O(T)} \left(\varepsilon_0+O\left(\sqrt{log(T)/n}\right)\right)$ for the target domain error, where $\varepsilon_0$ is the source domain error and $n$ is the data size of each domain. Due to the exponential factor, this upper bound becomes vacuous when $T$ is only moderately large. In this work, we analyze gradual self-training under more general and relaxed assumptions, and prove a significantly improved generalization bound as $\widetilde{O}\left(\varepsilon_0 + T\Delta + T/\sqrt{n} + 1/\sqrt{nT}\right)$, where $\Delta$ is the average distributional distance between consecutive domains. Compared with the existing bound with an exponential dependency on $T$ as a multiplicative factor, our bound only depends on $T$ linearly and additively. Perhaps more interestingly, our result implies the existence of an optimal choice of $T$ that minimizes the generalization error, and it also naturally suggests an optimal way to construct the path of intermediate domains so as to minimize the accumulative path length $T\Delta$ between the source and target. To corroborate the implications of our theory, we examine gradual self-training on multiple semi-synthetic and real datasets, which confirms our findings. We believe our insights provide a path forward toward the design of future GDA algorithms.

Author Information

Haoxiang Wang (University of Illinois Urbana-Champaign)

A Ph.D. student from UIUC, working on machine learning with theoretical guarantees.

Bo Li (UIUC)
Bo Li

Dr. Bo Li is an assistant professor in the Department of Computer Science at the University of Illinois at Urbana–Champaign. She is the recipient of the IJCAI Computers and Thought Award, Alfred P. Sloan Research Fellowship, AI’s 10 to Watch, NSF CAREER Award, MIT Technology Review TR-35 Award, Dean's Award for Excellence in Research, C.W. Gear Outstanding Junior Faculty Award, Intel Rising Star award, Symantec Research Labs Fellowship, Rising Star Award, Research Awards from Tech companies such as Amazon, Facebook, Intel, IBM, and eBay, and best paper awards at several top machine learning and security conferences. Her research focuses on both theoretical and practical aspects of trustworthy machine learning, which is at the intersection of machine learning, security, privacy, and game theory. She has designed several scalable frameworks for trustworthy machine learning and privacy-preserving data publishing. Her work has been featured by major publications and media outlets such as Nature, Wired, Fortune, and New York Times.

Han Zhao (University of Illinois at Urbana-Champaign)

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