嘈杂的中间尺度量子（NISQ）设备可以实现量子神经网络（QNN）的变异量子电路（VQC）。尽管基于VQC的QNN在许多机器学习任务中都取得了成功，但VQC的表示和泛化能力仍然需要进一步研究，尤其是在涉及经典输入的维度降低时。在这项工作中，我们首先提出了一个端到端量子神经网络，即TTN-VQC，该网络由基于张量训练网络（TTN）组成，用于降低维数和用于功能性回归的VQC。 。然后，我们旨在根据表示和泛化能力的TTN-VQC的错误性能分析。我们还通过利用polyak-lojasiewicz（PL）条件来表征TTN-VQC的优化属性。此外，我们在手写数字分类数据集上进行了功能回归的实验，以证明我们的理论分析是合理的。

量子计算机是下一代设备，有望执行超出古典计算机范围的计算。实现这一目标的主要方法是通过量子机学习，尤其是量子生成学习。由于量子力学的固有概率性质，因此可以合理地假设量子生成学习模型（QGLM）可能会超过其经典对应物。因此，QGLM正在从量子物理和计算机科学社区中受到越来越多的关注，在这些QGLM中，可以在近期量子机上有效实施各种QGLM，并提出了潜在的计算优势。在本文中，我们从机器学习的角度回顾了QGLM的当前进度。特别是，我们解释了这些QGLM，涵盖了量子电路出生的机器，量子生成的对抗网络，量子玻尔兹曼机器和量子自动编码器，作为经典生成学习模型的量子扩展。在这种情况下，我们探讨了它们的内在关系及其根本差异。我们进一步总结了QGLM在常规机器学习任务和量子物理学中的潜在应用。最后，我们讨论了QGLM的挑战和进一步研究指示。

Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing gradient problem in general deep quantum circuits. Specifically, we prove that under proper Gaussian initialized parameters, the norm of the gradient decays at most polynomially when the qubit number and the circuit depth increase. Our theoretical results hold for both the local and the global observable cases, where the latter was believed to have vanishing gradients even for very shallow circuits. Experimental results verify our theoretical findings in the quantum simulation and quantum chemistry.

Accurate determination of a small molecule candidate (ligand) binding pose in its target protein pocket is important for computer-aided drug discovery. Typical rigid-body docking methods ignore the pocket flexibility of protein, while the more accurate pose generation using molecular dynamics is hindered by slow protein dynamics. We develop a tiered tensor transform (3T) algorithm to rapidly generate diverse protein-ligand complex conformations for both pose and affinity estimation in drug screening, requiring neither machine learning training nor lengthy dynamics computation, while maintaining both coarse-grain-like coordinated protein dynamics and atomistic-level details of the complex pocket. The 3T conformation structures we generate are closer to experimental co-crystal structures than those generated by docking software, and more importantly achieve significantly higher accuracy in active ligand classification than traditional ensemble docking using hundreds of experimental protein conformations. 3T structure transformation is decoupled from the system physics, making future usage in other computational scientific domains possible.

We seek methods to model, control, and analyze robot teams performing environmental monitoring tasks. During environmental monitoring, the goal is to have teams of robots collect various data throughout a fixed region for extended periods of time. Standard bottom-up task assignment methods do not scale as the number of robots and task locations increases and require computationally expensive replanning. Alternatively, top-down methods have been used to combat computational complexity, but most have been limited to the analysis of methods which focus on transition times between tasks. In this work, we study a class of nonlinear macroscopic models which we use to control a time-varying distribution of robots performing different tasks throughout an environment. Our proposed ensemble model and control maintains desired time-varying populations of robots by leveraging naturally occurring interactions between robots performing tasks. We validate our approach at multiple fidelity levels including experimental results, suggesting the effectiveness of our approach to perform environmental monitoring.

Any strategy used to distribute a robot ensemble over a set of sequential tasks is subject to inaccuracy due to robot-level uncertainties and environmental influences on the robots' behavior. We approach the problem of inaccuracy during task allocation by modeling and controlling the overall ensemble behavior. Our model represents the allocation problem as a stochastic jump process and we regulate the mean and variance of such a process. The main contributions of this paper are: Establishing a structure for the transition rates of the equivalent stochastic jump process and formally showing that this approach leads to decoupled parameters that allow us to adjust the first- and second-order moments of the ensemble distribution over tasks, which gives the flexibility to decrease the variance in the desired final distribution. This allows us to directly shape the impact of uncertainties on the group allocation over tasks. We introduce a detailed procedure to design the gains to achieve the desired mean and show how the additional parameters impact the covariance matrix, which is directly associated with the degree of task allocation precision. Our simulation and experimental results illustrate the successful control of several robot ensembles during task allocation.

This paper focuses on the broadcast of information on robot networks with stochastic network interconnection topologies. Problematic communication networks are almost unavoidable in areas where we wish to deploy multi-robotic systems, usually due to a lack of environmental consistency, accessibility, and structure. We tackle this problem by modeling the broadcast of information in a multi-robot communication network as a stochastic process with random arrival times, which can be produced by irregular robot movements, wireless attenuation, and other environmental factors. Using this model, we provide and analyze a receding horizon control strategy to control the statistics of the information broadcast. The resulting strategy compels the robots to re-direct their communication resources to different neighbors according to the current propagation process to fulfill global broadcast requirements. Based on this method, we provide an approach to compute the expected time to broadcast the message to all nodes. Numerical examples are provided to illustrate the results.

We revisit the domain of off-policy policy optimization in RL from the perspective of coordinate ascent. One commonly-used approach is to leverage the off-policy policy gradient to optimize a surrogate objective -- the total discounted in expectation return of the target policy with respect to the state distribution of the behavior policy. However, this approach has been shown to suffer from the distribution mismatch issue, and therefore significant efforts are needed for correcting this mismatch either via state distribution correction or a counterfactual method. In this paper, we rethink off-policy learning via Coordinate Ascent Policy Optimization (CAPO), an off-policy actor-critic algorithm that decouples policy improvement from the state distribution of the behavior policy without using the policy gradient. This design obviates the need for distribution correction or importance sampling in the policy improvement step of off-policy policy gradient. We establish the global convergence of CAPO with general coordinate selection and then further quantify the convergence rates of several instances of CAPO with popular coordinate selection rules, including the cyclic and the randomized variants of CAPO. We then extend CAPO to neural policies for a more practical implementation. Through experiments, we demonstrate that CAPO provides a competitive approach to RL in practice.

Many real-world continuous control problems are in the dilemma of weighing the pros and cons, multi-objective reinforcement learning (MORL) serves as a generic framework of learning control policies for different preferences over objectives. However, the existing MORL methods either rely on multiple passes of explicit search for finding the Pareto front and therefore are not sample-efficient, or utilizes a shared policy network for coarse knowledge sharing among policies. To boost the sample efficiency of MORL, we propose Q-Pensieve, a policy improvement scheme that stores a collection of Q-snapshots to jointly determine the policy update direction and thereby enables data sharing at the policy level. We show that Q-Pensieve can be naturally integrated with soft policy iteration with convergence guarantee. To substantiate this concept, we propose the technique of Q replay buffer, which stores the learned Q-networks from the past iterations, and arrive at a practical actor-critic implementation. Through extensive experiments and an ablation study, we demonstrate that with much fewer samples, the proposed algorithm can outperform the benchmark MORL methods on a variety of MORL benchmark tasks.

Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables, acting on states of the dynamical system. This is ad hoc and requires the full dataset for evaluation. In this paper, we offer an optimization scheme to allow joint learning of the observables and Koopman operator with online data. Our results show we are able to reconstruct the evolution and represent the global features of complex dynamical systems.