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The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real…
In this paper we present the greedy step averaging(GSA) method, a parameter-free stochastic optimization algorithm for a variety of machine learning problems. As a gradient-based optimization method, GSA makes use of the information from…
In order to automate AI research we introduce a full, end-to-end framework, OMEGA: Optimizing Machine learning by Evaluating Generated Algorithms, that starts at idea generation and ends with executable code. Our system combines structured…
Neural networks trained with SGD were recently shown to rely preferentially on linearly-predictive features and can ignore complex, equally-predictive ones. This simplicity bias can explain their lack of robustness out of distribution…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
We give a new separation result between the generalization performance of stochastic gradient descent (SGD) and of full-batch gradient descent (GD) in the fundamental stochastic convex optimization model. While for SGD it is well-known that…
In Continual Learning settings, deep neural networks are prone to Catastrophic Forgetting. Orthogonal Gradient Descent was proposed to tackle the challenge. However, no theoretical guarantees have been proven yet. We present a theoretical…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…
Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…
One-class learning (OCL) comprises a set of techniques applied when real-world problems have a single class of interest. The usual procedure for OCL is learning a hypersphere that comprises instances of this class and, ideally, repels…
This paper establishes theoretical bonafides for implicit concurrent multivariate effect evaluation--implicit concurrency for short---a broad and versatile computational learning efficiency thought to underlie general-purpose, non-local,…
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG…
Orthogonal Gradient Descent (OGD) has emerged as a powerful method for continual learning. However, its Euclidean projections do not leverage the underlying information-geometric structure of the problem, which can lead to suboptimal…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
The inductive bias of a neural network is largely determined by the architecture and the training algorithm. To achieve good generalization, how to effectively train a neural network is of great importance. We propose a novel orthogonal…
Optimizing non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class…
In online learning an algorithm plays against an environment with losses possibly picked by an adversary at each round. The generality of this framework includes problems that are not adversarial, for example offline optimization, or saddle…
We consider a broad class of first-order optimization algorithms which are \emph{oblivious}, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as…
The main goal of this paper is twofold. First, we extend some results known in the case of weak greedy algorithms with a scalar parameter to the case of weak greedy algorithms with a weakness sequence. Second, we formulate a new setting of…