用量子神经切线核提升强化学习采样效率，实现低数据下更快收敛。
Quantum-Enhanced Neural Contextual Bandit Algorithms
- 通过冻结量子神经网络并使用其静态核进行岭回归，避免训练不稳问题。
- 理论证明在时间跨度T和动作数K下，参数量只需Ω((TK)^3)，远低于经典算法的Ω((TK)^8)。
- 适合研究量子机器学习与在线决策的学者，尤其关注低样本场景的性能突破。
随机上下文老虎机是序列决策的基础，但现有基于神经网络的算法在扩展至量子神经网络（QNN）时面临巨大挑战，如过度参数化、计算不稳定性及灾难性梯度消失现象。本文提出量子神经切线核-置信上界（QNTK-UCB）算法，利用量子神经切线核（QNTK）解决这些问题。通过在随机初始化后冻结QNN，并以静态的QNTK作为核进行岭回归，该方法绕过了显式参数化量子电路训练中的不稳定动态，同时充分利用了量子归纳偏置的独特优势。对于时间跨度$T$和动作数$K$，理论分析表明QNTK-UCB的参数量可缩减至$Ω((TK)^3)$，相较经典NeuralUCB算法所需的$Ω((TK)^8)$有显著降低。在非线性合成基准和量子原生变分量子本征求解器任务上的实证评估显示，该算法在低数据场景下具有更优的样本效率。研究表明，QNTK的固有特性提供了隐式正则化与更陡峭的谱衰减，为在线学习中实现‘量子优势’开辟了路径。
原文摘要 · Abstract (English)
Stochastic contextual bandits are fundamental for sequential decision-making but pose significant challenges for existing neural network-based algorithms, particularly when scaling to quantum neural networks (QNNs) due to issues such as massive over-parameterization, computational instability, and the barren plateau phenomenon. This paper introduces the Quantum Neural Tangent Kernel-Upper Confidence Bound (QNTK-UCB) algorithm, a novel algorithm that leverages the Quantum Neural Tangent Kernel (QNTK) to address these limitations. By freezing the QNN at a random initialization and utilizing its static QNTK as a kernel for ridge regression, QNTK-UCB bypasses the unstable training dynamics inherent in explicit parameterized quantum circuit training while fully exploiting the unique quantum inductive bias. For a time horizon $T$ and $K$ actions, our theoretical analysis reveals a significantly improved parameter scaling of $Ω((TK)^3)$ for QNTK-UCB, a substantial reduction compared to $Ω((TK)^8)$ required by classical NeuralUCB algorithms for similar regret guarantees. Empirical evaluations on non-linear synthetic benchmarks and quantum-native variational quantum eigensolver tasks demonstrate QNTK-UCB's superior sample efficiency in low-data regimes. This work highlights how the inherent properties of QNTK provide implicit regularization and a sharper spectral decay, paving the way for achieving ``quantum advantage'' in online learning.
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