Related papers: Randomized QLP algorithm and error analysis
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
We model equilibrium allocations in a distribution network as the solution of a linear program (LP) which minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that once a given node's supply…
Kernel ridge regression, in general, is expensive in memory allocation and computation time. This paper addresses low rank approximations and surrogates for kernel ridge regression, which bridge these difficulties. The fundamental…
This paper expands the analysis of randomized low-rank approximation beyond the Gaussian distribution to four classes of random matrices: (1) independent sub-Gaussian entries, (2) independent sub-Gaussian columns, (3) independent bounded…
We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an…
In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative…
Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates in particular enjoy many desirable…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
We study the Low Rank Phase Retrieval (LRPR) problem defined as follows: recover an $n \times q$ matrix $X^*$ of rank $r$ from a different and independent set of $m$ phaseless (magnitude-only) linear projections of each of its columns. To…
We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
The emergence of accurate open large language models (LLMs) has led to a race towards performant quantization techniques which can enable their execution on end-user devices. In this paper, we revisit the problem of "extreme" LLM…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren…
Quantum amplitude estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. Maximum-likelihood quantum amplitude estimation (MLQAE) is one of a…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…