Related papers: An efficient algorithm for positive realizations

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…

In this paper, we present and prove some results in multi-objective optimisation that are considered folklore. For the most part, proofs for these results exist in special cases, but they are used in more general settings since their proofs…

Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar…

Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…

We tackle the issue of finding a good policy when the number of policy updates is limited. This is done by approximating the expected policy reward as a sequence of concave lower bounds which can be efficiently maximized, drastically…

Transfer learning involves taking information and insight from one problem domain and applying it to a new problem domain. Although widely used in practice, theory for transfer learning remains less well-developed. To address this, we prove…

Building on insights of Jovanovic (1982) and subsequent authors, we develop a comprehensive theory of optimal timing of decisions based around continuation value functions and operators that act on them. Optimality results are provided…

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

Correlated outcomes are common in many practical problems. In some settings, one outcome is of particular interest, and others are auxiliary. To leverage information shared by all the outcomes, traditional multi-task learning (MTL)…

I discuss issues of inverting feasibly computable functions, optimal discovery algorithms, and the constant overheads in their performance.

A striking limitation of human cognition is our inability to execute some tasks simultaneously. Recent work suggests that such limitations can arise from a fundamental tradeoff in network architectures that is driven by the sharing of…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…

A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…

When humans perform inductive learning, they often enhance the process with background knowledge. With the increasing availability of well-formed collaborative knowledge bases, the performance of learning algorithms could be significantly…

We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…

A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…