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Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
CPU scheduling is the reason behind the performance of multiprocessing and in time-shared operating systems. Different scheduling criteria are used to evaluate Central Processing Unit Scheduling algorithms which are based on different…
In this paper, we present a work in progress about a deep learning based approach for automatic code optimization in polyhedral compilers. The proposed technique explores combinations of affine and non-affine loop transformations to find…
In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Consider a system consisting of multiple sockets into each of which a component is inserted. If a component fails, it is replaced immediately and system operation resumes. Then the failure process of the system is the superposition of…
We consider the challenge of finding a deterministic policy for a Markov decision process that uniformly (in all states) maximizes one reward subject to a probabilistic constraint over a different reward. Existing solutions do not fully…
The performance of reinforcement learning depends upon designing an appropriate action space, where the effect of each action is measurable, yet, granular enough to permit flexible behavior. So far, this process involved non-trivial user…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…
As the need for more computing power grows, traditional methods are hitting limits. To boost performance, we're expanding Central Processing Unit (CPU) capabilities and using specialized hardware accelerators. For example, mobile devices…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
In this paper, we propose a $p$-norm rule, which is a generalization of the steepest-edge rule, as a pivoting rule for the simplex method. For a nondegenerate linear programming problem, we show upper bounds for the number of iterations of…
Algorithmic recourse provides individuals who receive undesirable outcomes from machine learning systems with minimum-cost improvements to achieve a desirable outcome. However, machine learning models often get updated, so the recourse may…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
Computational protein structure determination involves optimization in a problem space much too large to exhaustively search. Existing approaches include optimization algorithms such as gradient descent and simulated annealing, but these…
Recent advancements in neural rendering technologies and their supporting devices have paved the way for immersive 3D experiences, significantly transforming human interaction with intelligent devices across diverse applications. However,…