In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher's instruction mechanism, can infer the teacher's intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn't been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher's cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements.

We address the problem of finding representative points of datasets by learning from multiple datasets and their ground-truth summaries. We develop a supervised subset selection framework, based on the facility location utility function, which learns to map datasets to their ground-truth representatives. To do so, we propose to learn representations of data so that the input of transformed data to the facility location recovers their ground-truth representatives. Given the NP-hardness of the utility function, we consider its convex relaxation based on sparse representation and investigate conditions under which the solution of the convex optimization recovers ground-truth representatives of each dataset. We design a loss function whose minimization over the parameters of the data representation network leads to satisfying the theoretical conditions, hence guaranteeing recovering ground-truth summaries. Given the non-convexity of the loss function, we develop an efficient learning scheme that alternates between representation learning by minimizing our proposed loss given the current assignments of points to ground-truth representatives and updating assignments given the current data representation. By experiments on the problem of learning key-steps (subactivities) of instructional videos, we show that our proposed framework improves the state-of-the-art supervised subset selection algorithms.

Energy based models (EBMs) are appealing due to their generality and simplicity in likelihood modeling, but have been traditionally difficult to train. We present techniques to scale MCMC based EBM training on continuous neural networks, and we show its success on the high-dimensional data domains of ImageNet32x32, ImageNet128x128, CIFAR-10, and robotic hand trajectories, achieving better samples than other likelihood models and nearing the performance of contemporary GAN approaches, while covering all modes of the data. We highlight some unique capabilities of implicit generation such as compositionality and corrupt image reconstruction and inpainting. Finally, we show that EBMs are useful models across a wide variety of tasks, achieving state-of-the-art out-of-distribution classification, adversarially robust classification, state-of-the-art continual online class learning, and coherent long term predicted trajectory rollouts.

Recent advances in graph neural networks (GNNs) have enabled more comprehensive modeling of molecules and molecular systems, thereby enhancing the precision of molecular property prediction and molecular simulations. Nonetheless, as the field has been progressing to bigger and more complex architectures, state-of-the-art GNNs have become largely prohibitive for many large-scale applications. In this paper, we explore the utility of knowledge distillation (KD) for accelerating molecular GNNs. To this end, we devise KD strategies that facilitate the distillation of hidden representations in directional and equivariant GNNs, and evaluate their performance on the regression task of energy and force prediction. We validate our protocols across different teacher-student configurations and datasets, and demonstrate that they can consistently boost the predictive accuracy of student models without any modifications to their architecture. Moreover, we conduct comprehensive optimization of various components of our framework, and investigate the potential of data augmentation to further enhance performance. All in all, we manage to close the gap in predictive accuracy between teacher and student models by as much as 96.7\% and 62.5\% for energy and force prediction respectively, while fully preserving the inference throughput of the more lightweight models.

In this paper, we consider a challenging but realistic continual learning problem, Few-Shot Continual Active Learning (FoCAL), where a CL agent is provided with unlabeled data for a new or a previously learned task in each increment and the agent only has limited labeling budget available. Towards this, we build on the continual learning and active learning literature and develop a framework that can allow a CL agent to continually learn new object classes from a few labeled training examples. Our framework represents each object class using a uniform Gaussian mixture model (GMM) and uses pseudo-rehearsal to mitigate catastrophic forgetting. The framework also uses uncertainty measures on the Gaussian representations of the previously learned classes to find the most informative samples to be labeled in an increment. We evaluate our approach on the CORe-50 dataset and on a real humanoid robot for the object classification task. The results show that our approach not only produces state-of-the-art results on the dataset but also allows a real robot to continually learn unseen objects in a real environment with limited labeling supervision provided by its user.

Stochastic composite mirror descent (SCMD) is a simple and efficient method able to capture both geometric and composite structures of optimization problems in machine learning. Existing strategies require to take either an average or a random selection of iterates to achieve optimal convergence rates, which, however, can either destroy the sparsity of solutions or slow down the practical training speed. In this paper, we propose a theoretically sound strategy to select an individual iterate of the vanilla SCMD, which is able to achieve optimal rates for both convex and strongly convex problems in a non-smooth learning setting. This strategy of outputting an individual iterate can preserve the sparsity of solutions which is crucial for a proper interpretation in sparse learning problems. We report experimental comparisons with several baseline methods to show the effectiveness of our method in achieving a fast training speed as well as in outputting sparse solutions.

We study the online learning with feedback graphs framework introduced by Mannor and Shamir (2011), in which the feedback received by the online learner is specified by a graph $G$ over the available actions. We develop an algorithm that simultaneously achieves regret bounds of the form: $O(\sqrt{\theta(G) T})$ with adversarial losses; $O(\theta(G)\mathrm{polylog}{T})$ with stochastic losses; and $O(\theta(G)\mathrm{polylog}{T} + \sqrt{\theta(G) C})$ with stochastic losses subject to $C$ adversarial corruptions. Here, $\theta(G)$ is the $clique~covering~number$ of the graph $G$. Our algorithm is an instantiation of Follow-the-Regularized-Leader with a novel regularization that can be seen as a product of a Tsallis entropy component (inspired by Zimmert and Seldin (2019)) and a Shannon entropy component (analyzed in the corrupted stochastic case by Amir et al. (2020)), thus subtly interpolating between the two forms of entropies. One of our key technical contributions is in establishing the convexity of this regularizer and controlling its inverse Hessian, despite its complex product structure.

In this work we consider an online learning problem, called Online $k$-Clustering with Moving Costs, at which a learner maintains a set of $k$ facilities over $T$ rounds so as to minimize the connection cost of an adversarially selected sequence of clients. The learner is informed on the positions of the clients at each round $t$ only after its facility-selection and can use this information to update its decision in the next round. However, updating the facility positions comes with an additional moving cost based on the moving distance of the facilities. We present the first $\mathcal{O}(\log n)$-regret polynomial-time online learning algorithm guaranteeing that the overall cost (connection $+$ moving) is at most $\mathcal{O}(\log n)$ times the time-averaged connection cost of the best fixed solution. Our work improves on the recent result of (Fotakis et al., 2021) establishing $\mathcal{O}(k)$-regret guarantees only on the connection cost.

We consider online optimization over Riemannian manifolds, where a learner attempts to minimize a sequence of time-varying loss functions defined on Riemannian manifolds. Though many Euclidean online convex optimization algorithms have been proven useful in a wide range of areas, less attention has been paid to their Riemannian counterparts. In this paper, we study Riemannian online gradient descent (R-OGD) on Hadamard manifolds for both geodesically convex and strongly geodesically convex loss functions, and Riemannian bandit algorithm (R-BAN) on Hadamard homogeneous manifolds for geodesically convex functions. We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension. We also find a universal lower bound for the achievable regret by constructing an online convex optimization problem on Hadamard manifolds. All the obtained regret bounds match the corresponding results are provided in Euclidean spaces.

We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) by distilling knowledge from a teacher GNN model trained on a complete graph to a student GNN model operating on a smaller or sparser graph. To this end, we revisit the connection between thermodynamics and the behavior of GNN, based on which we propose Neural Heat Kernel (NHK) to encapsulate the geometric property of the underlying manifold concerning the architecture of GNNs. A fundamental and principled solution is derived by aligning NHKs on teacher and student models, dubbed as Geometric Knowledge Distillation. We develop non-and parametric instantiations and demonstrate their efficacy in various experimental settings for knowledge distillation regarding different types of privileged topological information and teacher-student schemes.