In this paper, we study the generalization properties of Model-Agnostic Meta-Learning (MAML) algorithms for supervised learning problems. We focus on the setting in which we train the MAML model over $m$ tasks, each with $n$ data points, and characterize its generalization error from two points of view: First, we assume the new task at test time is one of the training tasks, and we show that, for strongly convex objective functions, the expected excess population loss is bounded by $\mathcal{O}(1/mn)$. Second, we consider the MAML algorithm's generalization to an unseen task and show that the resulting generalization error depends on the total variation distance between the underlying distributions of the new task and the tasks observed during the training process. Our proof techniques rely on the connections between algorithmic stability and generalization bounds of algorithms. In particular, we propose a new definition of stability for meta-learning algorithms, which allows us to capture the role of both the number of tasks $m$ and number of samples per task $n$ on the generalization error of MAML.

In this work we study generalization guarantees for the metric learning problem, where the metric is induced by a neural network type embedding of the data. Specifically, we provide uniform generalization bounds for two regimes -- the sparse regime, and a non-sparse regime which we term \emph{bounded amplification}. The sparse regime bounds correspond to situations where $\ell_1$-type norms of the parameters are small. Similarly to the situation in classification, solutions satisfying such bounds can be obtained by an appropriate regularization of the problem. On the other hand, unregularized SGD optimization of a metric learning loss typically does not produce sparse solutions. We show that despite this lack of sparsity, by relying on a different, new property of the solutions, it is still possible to provide dimension free generalization guarantees. Consequently, these bounds can explain generalization in non sparse real experimental situations. We illustrate the studied phenomena on the MNIST and 20newsgroups datasets.

We study the problem of Online Convex Optimization (OCO) with memory, which allows loss functions to depend on past decisions and thus captures temporal effects of learning problems. In this paper, we introduce dynamic policy regret as the performance measure to design algorithms robust to non-stationary environments, which competes algorithms' decisions with a sequence of changing comparators. We propose a novel algorithm for OCO with memory that provably enjoys an optimal dynamic policy regret. The key technical challenge is how to control the switching cost, the cumulative movements of player's decisions, which is neatly addressed by a novel decomposition of dynamic policy regret and an appropriate meta-expert structure. Furthermore, we generalize the results to the problem of online non-stochastic control, i.e., controlling a linear dynamical system with adversarial disturbance and convex loss functions. We derive a novel gradient-based controller with dynamic policy regret guarantees, which is the first controller competitive to a sequence of changing policies.

By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably approximately correct (PAC) Bayes bound theory provides a theoretical framework to analyze the generalization performance for meta-learning. We derive three novel generalisation error bounds for meta-learning based on PAC-Bayes relative entropy bound. Furthermore, using the empirical risk minimization (ERM) method, a PAC-Bayes bound for meta-learning with data-dependent prior is developed. Experiments illustrate that the proposed three PAC-Bayes bounds for meta-learning guarantee a competitive generalization performance guarantee, and the extended PAC-Bayes bound with data-dependent prior can achieve rapid convergence ability.

The goal of few-shot learning is to learn a classifier that can recognize unseen classes from limited support data with labels. A common practice for this task is to train a model on the base set first and then transfer to novel classes through fine-tuning (Here fine-tuning procedure is defined as transferring knowledge from base to novel data, i.e. learning to transfer in few-shot scenario.) or meta-learning. However, as the base classes have no overlap to the novel set, simply transferring whole knowledge from base data is not an optimal solution since some knowledge in the base model may be biased or even harmful to the novel class. In this paper, we propose to transfer partial knowledge by freezing or fine-tuning particular layer(s) in the base model. Specifically, layers will be imposed different learning rates if they are chosen to be fine-tuned, to control the extent of preserved transferability. To determine which layers to be recast and what values of learning rates for them, we introduce an evolutionary search based method that is efficient to simultaneously locate the target layers and determine their individual learning rates. We conduct extensive experiments on CUB and mini-ImageNet to demonstrate the effectiveness of our proposed method. It achieves the state-of-the-art performance on both meta-learning and non-meta based frameworks. Furthermore, we extend our method to the conventional pre-training + fine-tuning paradigm and obtain consistent improvement.

State-of-the-art deep-learning systems use decision rules that are challenging for humans to model. Explainable AI (XAI) attempts to improve human understanding but rarely accounts for how people typically reason about unfamiliar agents. We propose explicitly modeling the human explainee via Bayesian Teaching, which evaluates explanations by how much they shift explainees' inferences toward a desired goal. We assess Bayesian Teaching in a binary image classification task across a variety of contexts. Absent intervention, participants predict that the AI's classifications will match their own, but explanations generated by Bayesian Teaching improve their ability to predict the AI's judgements by moving them away from this prior belief. Bayesian Teaching further allows each case to be broken down into sub-examples (here saliency maps). These sub-examples complement whole examples by improving error detection for familiar categories, whereas whole examples help predict correct AI judgements of unfamiliar cases.

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Previous post: ML theory with bad drawings Next post: TBD, see also all seminar posts and course webpage. Lecture video (starts in slide 2 since I hit record button 30 seconds too late – sorry!) These are rough notes for the first lecture in my advanced topics in machine learning seminar. See the previous post for the introduction. This lecture's focus was on "classical" learing theory.

The Garrison (armies of militia) of libraries worldwide offer millions of books, such as the Library of Congress in D.C. has over 162 million books, and the New York Public library carries around 53 million books. A number of people have asked me through several of my channels and conferences -- how to find time to read books, and what can be done to read more books each month. Some audiences even feel that 43 machine learning books in a year are insufficient, and want more. I keep discovering new material every day on top of the antiquated books, which still offer good concepts. To get started, I would suggest disconnecting from Netflix, Amazon Video, and regular TV channels.