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ItemFast Rate Generalization Error Bounds: Variations on a Theme(IEEE, 2022)A recent line of works, initiated by [1] and [2], has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected generalization error is in the form of O(\sqrt λ I/n ) where λ is an assumption-dependent coefficient and I is some information-Theoretic quantities such as the mutual information between the data sample and the learned hypothesis. However, such a learning rate is typically considered to be "slow", compared to a "fast rate"of O(1 /n) in many learning scenarios. In this work, we first show that the square root does not necessarily imply a slow rate, and a fast rate result can still be obtained using this bound by evaluating λ under an appropriate assumption. Furthermore, we identify the key conditions needed for the fast rate generalization error, which we call the ( η, c)-central condition. Under this condition, we give information-Theoretic bounds on the generalization error and excess risk, with a convergence rate of O (1 /n) for specific learning algorithms such as empirical risk minimization. Finally, analytical examples are given to show the effectiveness of the bounds.
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ItemOnline Transfer Learning: Negative Transfer and Effect of Prior Knowledge(IEEE, 2021-07-12)Transfer learning is a machine learning paradigm where the knowledge from one task is utilized to resolve the problem in a related task. On the one hand, it is conceivable that knowledge from one task could be useful for solving a related problem. On the other hand, it is also recognized that if not executed properly, transfer learning algorithms could in fact impair the learning performance instead of improving it - commonly known as negative transfer. In this paper, we study the online transfer learning problems where the source samples are given in an off-line way while the target samples arrive sequentially. We define the expected regret of the online transfer learning problem, and provide upper bounds on the regret using information-theoretic quantities. We also obtain exact expressions for the bounds when the sample size becomes large. Examples show that the derived bounds are accurate even for small sample sizes. Furthermore, the obtained bounds give valuable insight on the effect of prior knowledge for transfer learning in our formulation. In particular, we formally characterize the conditions under which negative transfer occurs.
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ItemInformation-theoretic analysis for transfer learning(IEEE, 2020)Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different distributions (denoted as μ and μ', respectively). In this work, we give an informationtheoretic analysis on the generalization error and the excess risk of transfer learning algorithms, following a line of work initiated by Russo and Zhou. Our results suggest, perhaps as expected, that the Kullback-Leibler (KL) divergence D(μμ') plays an important role in characterizing the generalization error in the settings of domain adaptation. Specifically, we provide generalization error upper bounds for general transfer learning algorithms, and extend the results to a specific empirical risk minimization (ERM) algorithm where data from both distributions are available in the training phase. We further apply the method to iterative, noisy gradient descent algorithms, and obtain upper bounds which can be easily calculated, only using parameters from the learning algorithms. A few illustrative examples are provided to demonstrate the usefulness of the results. In particular, our bound is tighter in specific classification problems than the bound derived using Rademacher complexity.