Search Results for author: Tongyang Li

Found 9 papers, 1 papers with code

Escape saddle points by a simple gradient-descent based algorithm

no code implementations NeurIPS 2021 Chenyi Zhang, Tongyang Li

Compared to the previous state-of-the-art algorithms by Jin et al. with $\tilde{O}((\log n)^{4}/\epsilon^{2})$ or $\tilde{O}((\log n)^{6}/\epsilon^{1. 75})$ iterations, our algorithm is polynomially better in terms of $\log n$ and matches their complexities in terms of $1/\epsilon$.

Sublinear classical and quantum algorithms for general matrix games

no code implementations11 Dec 2020 Tongyang Li, Chunhao Wang, Shouvanik Chakrabarti, Xiaodi Wu

We give a sublinear classical algorithm that can interpolate smoothly between these two cases: for any fixed $q\in (1, 2]$, we solve the matrix game where $\mathcal{X}$ is a $\ell_{q}$-norm unit ball within additive error $\epsilon$ in time $\tilde{O}((n+d)/{\epsilon^{2}})$.

Quantum algorithms for escaping from saddle points

no code implementations20 Jul 2020 Chenyi Zhang, Jiaqi Leng, Tongyang Li

Compared to the classical state-of-the-art algorithm by Jin et al. with $\tilde{O}(\log^{6} (n)/\epsilon^{1. 75})$ queries to the gradient oracle (i. e., the first-order oracle), our quantum algorithm is polynomially better in terms of $\log n$ and matches its complexity in terms of $1/\epsilon$.

Quantum exploration algorithms for multi-armed bandits

no code implementations14 Jul 2020 Daochen Wang, Xuchen You, Tongyang Li, Andrew M. Childs

Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization.

Multi-Armed Bandits

Quantum Wasserstein Generative Adversarial Networks

1 code implementation NeurIPS 2019 Shouvanik Chakrabarti, Yiming Huang, Tongyang Li, Soheil Feizi, Xiaodi Wu

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines.

Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning

no code implementations14 Oct 2019 Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, Chunhao Wang

Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en et al. [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions.

Recommendation Systems

Sublinear quantum algorithms for training linear and kernel-based classifiers

no code implementations4 Apr 2019 Tongyang Li, Shouvanik Chakrabarti, Xiaodi Wu

We design sublinear quantum algorithms for the same task running in $\tilde{O}(\sqrt{n} +\sqrt{d})$ time, a quadratic improvement in both $n$ and $d$.

Quantization

Distributional property testing in a quantum world

no code implementations2 Feb 2019 András Gilyén, Tongyang Li

The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.

Learning Theory

Quantum-inspired sublinear algorithm for solving low-rank semidefinite programming

no code implementations10 Jan 2019 Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, Chunhao Wang

In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank constraints; specifically, given an SDP with $m$ constraint matrices, each of dimension $n$ and rank $r$, our algorithm can compute any entry and efficient descriptions of the spectral decomposition of the solution matrix.

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