Related papers: The Oval Strikes Back
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap.…
Private information retrieval (PIR) gets renewed attentions due to its information-theoretic reformulation and its application in distributed storage system (DSS). The general PIR model considers a coded database containing $N$ servers…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded…
Design structure matrices (DSMs) are useful to represent high-level system structure, modeling interactions between design entities. DSMs are used for many visualization and abstraction activities. In this work, we propose the use of an…
Modern computer systems are characterized by deep memory hierarchies, composed of main memory, multiple layers of cache, and other specialized types of memory. In parallel and distributed systems, additional memory layers are added to this…
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…
We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…
Sparse representations have been successfully applied to signal processing, computer vision and machine learning. Currently there is a trend to learn sparse models directly on structure data, such as region covariance. However, such methods…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…
Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…
We study episodic reinforcement learning in non-stationary linear (a.k.a. low-rank) Markov Decision Processes (MDPs), i.e, both the reward and transition kernel are linear with respect to a given feature map and are allowed to evolve either…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…