Consider the task of learning an unknown concept from a given concept class; to what extent does interacting with a domain expert accelerate the learning process? It is common to measure the effectiveness of learning algorithms by plotting the learning curve, that is, the decay of the error rate as a function of the algorithm's resources (examples, queries, etc). Thus, the overarching question in this work is whether (and which kind of) interaction accelerates the learning curve. Previous work in interactive learning focused on uniform bounds on the learning rates which only capture the upper envelope of the learning curves over families of data distributions. We thus formalize our overarching question within the distribution dependent framework of universal learning, which aims to understand the performance of learning algorithms on every data distribution, but without requiring a single upper bound which applies uniformly to all distributions. Our main result reveals a fundamental trichotomy of interactive learning rates, thus providing a complete characterization of universal interactive learning. As a corollary we deduce a strong affirmative answer to our overarching question, showing that interaction is beneficial. Remarkably, we show that in important cases such benefits are realized with label queries, that is, by active learning algorithms. On the other hand, our lower bounds apply to arbitrary binary queries and, hence, they hold in any interactive learning setting.

This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret bounds for stochastic environments. As Alon et al. [2015] have shown, tight regret bounds depend on the structure of the feedback graph: strongly observable graphs yield minimax regret of $\tilde{\Theta}( \alpha^{1/2} T^{1/2})$, while weakly observable graphs induce minimax regret of $\tilde{\Theta}( \delta^{1/3} T^{2/3})$, where $\alpha$ and $\delta$, respectively, represent the independence number of the graph and the domination number of a certain portion of the graph.

In this paper, we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial learning problem can be transformed into a minimax statistical learning problem by introducing a transport map between distributions. Then, we prove a new risk bound for this minimax problem in terms of covering numbers under a weak version of Lipschitz condition. Our method can be applied to multi-class classification and popular loss functions including the hinge loss and ramp loss. As some illustrative examples, we derive the adversarial risk bounds for SVMs and deep neural networks, and our bounds have two data-dependent terms, which can be optimized for achieving adversarial robustness.

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.

Online learning methods, like the seminal Passive-Aggressive (PA) classifier, are still highly effective for high-dimensional streaming data, out-of-core processing, and other throughput-sensitive applications. Many such algorithms rely on fast adaptation to individual errors as a key to their convergence. While such algorithms enjoy low theoretical regret, in real-world deployment they can be sensitive to individual outliers that cause the algorithm to over-correct. When such outliers occur at the end of the data stream, this can cause the final solution to have unexpectedly low accuracy. We design a weighted reservoir sampling (WRS) approach to obtain a stable ensemble model from the sequence of solutions without requiring additional passes over the data, hold-out sets, or a growing amount of memory. Our key insight is that good solutions tend to be error-free for more iterations than bad solutions, and thus, the number of passive rounds provides an estimate of a solution's relative quality. Our reservoir thus contains $K$ previous intermediate weight vectors with high survival times. We demonstrate our WRS approach on the Passive-Aggressive Classifier (PAC) and First-Order Sparse Online Learning (FSOL), where our method consistently and significantly outperforms the unmodified approach. We show that the risk of the ensemble classifier is bounded with respect to the regret of the underlying online learning method.

Humans are autotelic agents who learn by setting and pursuing their own goals. However, the precise mechanisms guiding human goal selection remain unclear. Learning progress, typically measured as the observed change in performance, can provide a valuable signal for goal selection in both humans and artificial agents. We hypothesize that human choices of goals may also be driven by, which humans can estimate through knowledge of their actions and the environment - even without experiencing immediate changes in performance. To test this hypothesis, we designed a hierarchical reinforcement learning task in which human participants (N = 175) repeatedly chose their own goals and learned goal-conditioned policies. Our behavioral and computational modeling results confirm the influence of latent learning progress on goal selection and uncover inter-individual differences, partially mediated by recognition of the task's hierarchical structure. By investigating the role of latent learning progress in human goal selection, we pave the way for more effective and personalized learning experiences as well as the advancement of more human-like autotelic machines.

We study an online classification problem with partial feedback in which individuals arrive one at a time from a fixed but unknown distribution, and must be classified as positive or negative. Our algorithm only observes the true label of an individual if they are given a positive classification. This setting captures many classification problems for which fairness is a concern: for example, in criminal recidivism prediction, recidivism is only observed if the inmate is released; in lending applications, loan repayment is only observed if the loan is granted. We require that our algorithms satisfy common statistical fairness constraints (such as equalizing false positive or negative rates --- introduced as equal opportunity in Hardt et al. (2016)) at every round, with respect to the underlying distribution. We give upper and lower bounds characterizing the cost of this constraint in terms of the regret rate (and show that it is mild), and give an oracle efficient algorithm that achieves the upper bound.

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), that learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f.

A current remarkable improvement of unsupervised visual representation learning is based on heavy networks with large-batch training. While recent methods have greatly reduced the gap between supervised and unsupervised performance of deep models such as ResNet-50, this development has been relatively limited for small models. In this work, we propose a novel unsupervised learning framework for small networks that combines deep self-supervised representation learning and knowledge distillation within one-phase training. In particular, a teacher model is trained to produce consistent cluster assignments between different views of the same image. Simultaneously, a student model is encouraged to mimic the prediction of on-the-fly self-supervised teacher. For effective knowledge transfer, we adopt the idea of domain classifier so that student training is guided by discriminative features invariant to the representational space shift between teacher and student. We also introduce a network driven multi-view generation paradigm to capture rich feature information contained in the network itself. Extensive experiments show that our student models surpass state-of-the-art offline distilled networks even from stronger self-supervised teachers as well as top-performing self-supervised models. Notably, our ResNet-18, trained with ResNet-50 teacher, achieves 68.3% ImageNet Top-1 accuracy on frozen feature linear evaluation, which is only 1.5% below the supervised baseline.

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ \emph{worst case} regret guarantee for both convex and nonconvex losses. In this work, we show that when the sequence of loss functions is \emph{predictable}, a simple modification of FTPL which incorporates optimism can achieve better regret guarantees, while retaining the optimal worst-case regret guarantee for unpredictable sequences. A key challenge in obtaining these tighter regret bounds is the stochasticity and optimism in the algorithm, which requires different analysis techniques than those commonly used in the analysis of FTPL. The key ingredient we utilize in our analysis is the dual view of perturbation as regularization.