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While online bipartite matching has gained significant attention in recent years, existing analyses in stochastic settings fail to capture the performance of algorithms on heterogeneous graphs, such as those incorporating inter-group…
Fast and precise Lipschitz constant estimation of neural networks is an important task for deep learning. Researchers have recently found an intrinsic trade-off between the accuracy and smoothness of neural networks, so training a network…
Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…
Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
We show that convex-concave Lipschitz stochastic saddle point problems (also known as stochastic minimax optimization) can be solved under the constraint of $(\epsilon,\delta)$-differential privacy with \emph{strong (primal-dual) gap} rate…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…
Fairness has emerged as a formidable challenge in data-driven decisions. Many of the data problems, such as creating compact data summaries for approximate query processing, can be effectively tackled using concepts from computational…
Safety-critical applications are required to perform as expected in normal operations. Image processing functions are often required to be insensitive to small geometric perturbations such as rotation, scaling, shearing or translation. This…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
In the stochastic online vector balancing problem, vectors $v_1,v_2,\ldots,v_T$ chosen independently from an arbitrary distribution in $\mathbb{R}^n$ arrive one-by-one and must be immediately given a $\pm$ sign. The goal is to keep the norm…
The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…
This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator). We first consider $\gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space…
Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this…