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Chaowen Guan

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3 papers

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AAAI Conference 2026 Conference Paper

Quantum Non-Linear Bandit Optimization

Zakaria Shams Siam
Chaowen Guan
Chong Liu

We study non-linear bandit optimization where the learner maximizes a black-box function with zeroth order function oracle, which has been successfully applied in many critical applications such as drug discovery and materials design. Existing works have showed that with the aid of quantum computing, it is possible to break the classical Ω(√T) regret lower bound and achieve the new O(poly log T) upper bound. However, they usually assume that the objective function sits within the reproducing kernel Hilbert space and their algorithms suffer from the curse of dimensionality. In this paper, we propose the new Q-NLB-UCB algorithm which enjoys an input dimension-free O(poly log T) upper bound, making it applicable for high-dimensional tasks. At the heart of our algorithm design are quantum Monte Carlo mean estimator, parametric function approximation technique, and a new quantum non-linear regression oracle, which can be of independent interests in more quantum machine learning problems. Our algorithm is also validated for its efficiency compared with other quantum algorithms on both high-dimensional synthetic and real-world tasks.

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NeurIPS Conference 2024 Conference Paper

Quantum Algorithms for Non-smooth Non-convex Optimization

Chengchang Liu
Chaowen Guan
Jianhao He
John C. Lui

This paper considers the problem for finding the $(\delta, \epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a novel zeroth-order quantum estimator for the gradient of the smoothed surrogate. Based on such estimator, we propose a novel quantum algorithm that achieves a query complexity of $\tilde{\mathcal{O}}(d^{3/2}\delta^{-1}\epsilon^{-3})$ on the stochastic function value oracle, where $d$ is the dimension of the problem. We also enhance the query complexity to $\tilde{\mathcal{O}}(d^{3/2}\delta^{-1}\epsilon^{-7/3})$ by introducing a variance reduction variant. Our findings demonstrate the clear advantages of utilizing quantum techniques for non-convex non-smooth optimization, as they outperform the optimal classical methods on the dependency of $\epsilon$ by a factor of $\epsilon^{-2/3}$.

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AAAI Conference 2020 Conference Paper

Estimating Stochastic Linear Combination of Non-Linear Regressions

Di Wang
Xiangyu Guo
Chaowen Guan
Shi Li
Jinhui Xu

In this paper we study the problem of estimating stochastic linear combination of non-linear regressions, which has a close connection with many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefﬁcient Index Models and Two-layer Neural Networks. Speciﬁcally, we ﬁrst show that with some mild assumptions, if the variate vector x is multivariate Gaussian, then there is an algorithm whose output vectors have 2-norm estimation errors of O( p n ) with high probability, where p is the dimension of x and n is the number of samples. Then we extend our result to the case where x is sub-Gaussian using the zero-bias transformation, which could be seen as a generalization of the classic Stein’s lemma. We also show that with some additional assumptions there is an algorithm whose output vectors have ∞-norm estimation errors of O( 1 √ p + p n ) with high probability. Finally, for both Gaussian and sub-Gaussian cases we propose a faster sub-sampling based algorithm and show that when the sub-sample sizes are large enough then the estimation errors will not be sacriﬁced by too much. Experiments for both cases support our theoretical results. To the best of our knowledge, this is the ﬁrst work that studies and provides theoretical guarantees for the stochastic linear combination of non-linear regressions model.

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