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Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…
Online mirror descent (OMD) is a fundamental algorithmic paradigm that underlies many algorithms in optimization, machine learning and sequential decision-making. The OMD iterates are defined as solutions to optimization subproblems which,…
We propose a voted dual averaging method for online classification problems with explicit regularization. This method employs the update rule of the regularized dual averaging (RDA) method, but only on the subsequence of training examples…
Online allocation problems with resource constraints have a rich history in operations research. In this paper, we introduce the \emph{regularized online allocation problem}, a variant that includes a non-linear regularizer acting on the…
We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…
In the field of online sequential decision-making, we address the problem with delays utilizing the framework of online convex optimization (OCO), where the feedback of a decision can arrive with an unknown delay. Unlike previous research…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application…
Partially Observable Markov Decision Processes (POMDPs) are a powerful framework for planning under uncertainty. They allow to model state uncertainty as a belief probability distribution. Approximate solvers based on Monte Carlo sampling…
This paper studies an optimization problem on the sum of traces of matrix quadratic forms on $m$ orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the paper…
We present a new framework for deriving bounds on the generalization bound of statistical learning algorithms from the perspective of online learning. Specifically, we construct an online learning game called the "generalization game",…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
This paper aims at solving the Hermitian SDC problem, i.e., that of \textit{simultaneously diagonalizing via $*$-congruence} a collection of finitely many (not need pairwise commute) Hermitian matrices. Theoretically, we provide some…
In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
Reinforcement learning with outcome-based feedback faces a fundamental challenge: when rewards are only observed at trajectory endpoints, how do we assign credit to the right actions? This paper provides the first comprehensive analysis of…
The commonly adopted assumption of stationary demands cannot actually reflect fluctuating demands and will weaken solution effectiveness in real practice. We consider an On-line Non-stationary Inventory Control Problem (ONICP), in which no…