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In this paper, we provide a comprehensive theoretical analysis of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak Heavy-Ball and Nesterov) for tracking time-varying optima under strong convexity and smoothness. Our…
We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the…
We develop a first-order (pseudo-)gradient approach for optimizing functions over the stationary distribution of discrete-time Markov chains (DTMC). We give insights into why solving this optimization problem is challenging and show how…
Big data analytics on geographically distributed datasets (across data centers or clusters) has been attracting increasing interests from both academia and industry, but also significantly complicates the system and algorithm designs. In…
Recent breakthroughs in generative artificial intelligence have triggered a surge in demand for machine learning training, which poses significant cost burdens and environmental challenges due to its substantial energy consumption.…
There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in…
We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…
In cloud computing paradigm, virtual resource autoscaling approaches have been intensively studied recent years. Those approaches dynamically scale in/out virtual resources to adjust system performance for saving operation cost. However,…
While $\mathcal{H}_\infty$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between…
One practical open problem is the development of a distributed algorithm that achieves near-optimal utility using only a finite (and small) buffer size for queues in a stochastic network. This paper studies utility maximization (or cost…
Cloud computing has motivated renewed interest in resource allocation problems with new consumption models. A common goal is to share a resource, such as CPU or I/O bandwidth, among distinct users with different demand patterns as well as…
In this paper, we first remodel the line coverage as a 1D discrete problem with co-linear targets. Then, an order-based greedy algorithm, called OGA, is proposed to solve the problem optimally. It will be shown that the existing order in…
The exponential growth of data necessitates distributed storage models, such as peer-to-peer systems and data federations. While distributed storage can reduce costs and increase reliability, the heterogeneity in storage capacity, I/O…
We study the repair problem of distributed storage systems in erasure networks where the packets transmitted from surviving nodes to the new node might be lost. The fundamental storage-bandwidth tradeoff is calculated by multicasting…
Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses $N$ scenarios (design samples), followed by randomized feasibility phase that uses $N_o$…
Cloud computing infrastructures increasingly rely on geographically distributed data centers to meet the growing demand for low latency, high availability, and cost-efficient service delivery. In this context, load balancing plays a…
Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
Grid-based storage systems with uniformly shaped loads (e.g., containers, pallets, totes) are commonplace in logistics, industrial, and transportation domains. A key performance metric for such systems is the maximization of space…
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…