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We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
Hoffman's classical result gives a bound on the distance of a point from a convex and compact polytope in terms of the magnitude of violation of the constraints. Recently, several results showed that Hoffman's bound can be used to derive…
Reinforcement learning-based methods for constructing solutions to combinatorial optimization problems are rapidly approaching the performance of human-designed algorithms. To further narrow the gap, learning-based approaches must…
One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation…
The NP-hard problem of optimizing a shallow ReLU network can be characterized as a combinatorial search over each training example's activation pattern followed by a constrained convex problem given a fixed set of activation patterns. We…
We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We…
Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest improvement an…
Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…
Online learning holds the promise of enabling efficient long-term credit assignment in recurrent neural networks. However, current algorithms fall short of offline backpropagation by either not being scalable or failing to learn long-range…
The extension of classical online algorithms when provided with predictions is a new and active research area. In this paper, we extend the primal-dual method for online algorithms in order to incorporate predictions that advise the online…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
We provide algorithms that guarantee regret $R_T(u)\le \tilde O(G\|u\|^3 + G(\|u\|+1)\sqrt{T})$ or $R_T(u)\le \tilde O(G\|u\|^3T^{1/3} + GT^{1/3}+ G\|u\|\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison…
Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear…
Follow-the-Regularized-Leader (FTRL) algorithms are a popular class of learning algorithms for online linear optimization (OLO) that guarantee sub-linear regret, but the choice of regularizer can significantly impact dimension-dependent…
We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
It is increasingly common to solve combinatorial optimisation problems that are partially-specified. We survey the case where the objective function or the relations between variables are not known or are only partially specified. The…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…