The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments.

Decentralized Federated Learning (DFL) has received significant recent research attention, capturing settings where both model updates and model aggregations -- the two key FL processes -- are conducted by the clients. In this work, we propose Decentralized Sporadic Federated Learning ($\texttt{DSpodFL}$), a DFL methodology which generalizes the notion of sporadicity in both of these processes, modeling the impact of different forms of heterogeneity that manifest in realistic DFL settings. $\texttt{DSpodFL}$ unifies many of the prominent decentralized optimization methods, e.g., distributed gradient descent (DGD), randomized gossip (RG), and decentralized federated averaging (DFedAvg), under a single modeling framework. We analytically characterize the convergence behavior of $\texttt{DSpodFL}$, showing, among other insights, that we can match a geometric convergence rate to a finite optimality gap under more general assumptions than in existing works. Through experiments, we demonstrate that $\texttt{DSpodFL}$ achieves significantly improved training speeds and robustness to variations in system parameters compared to the state-of-the-art.

Recent advances in diffusion models attempt to handle conditional generative tasks by utilizing a differentiable loss function for guidance without the need for additional training. While these methods achieved certain success, they often compromise on sample quality and require small guidance step sizes, leading to longer sampling processes. This paper reveals that the fundamental issue lies in the manifold deviation during the sampling process when loss guidance is employed. We theoretically show the existence of manifold deviation by establishing a certain lower bound for the estimation error of the loss guidance. To mitigate this problem, we propose Diffusion with Spherical Gaussian constraint (DSG), drawing inspiration from the concentration phenomenon in high-dimensional Gaussian distributions. DSG effectively constrains the guidance step within the intermediate data manifold through optimization and enables the use of larger guidance steps. Furthermore, we present a closed-form solution for DSG denoising with the Spherical Gaussian constraint. Notably, DSG can seamlessly integrate as a plugin module within existing training-free conditional diffusion methods. Implementing DSG merely involves a few lines of additional code with almost no extra computational overhead, yet it leads to significant performance improvements. Comprehensive experimental results in various conditional generation tasks validate the superiority and adaptability of DSG in terms of both sample quality and time efficiency.

Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is minimized with respect to a given input, rather than optimizing for the worst case. However, optimal adaptive quantization methods are considered infeasible in terms of both their runtime and memory requirements. We revisit the Adaptive Vector Quantization (AVQ) problem and present algorithms that find optimal solutions with asymptotically improved time and space complexity. We also present an even faster near-optimal algorithm for large inputs. Our experiments show our algorithms may open the door to using AVQ more extensively in a variety of machine learning applications.

Bayesian Optimization (BO) is an effective method for finding the global optimum of expensive black-box functions. However, it is well known that applying BO to high-dimensional optimization problems is challenging. To address this issue, a promising solution is to use a local search strategy that partitions the search domain into local regions with high likelihood of containing the global optimum, and then use BO to optimize the objective function within these regions. In this paper, we propose a novel technique for defining the local regions using the Covariance Matrix Adaptation (CMA) strategy. Specifically, we use CMA to learn a search distribution that can estimate the probabilities of data points being the global optimum of the objective function. Based on this search distribution, we then define the local regions consisting of data points with high probabilities of being the global optimum. Our approach serves as a meta-algorithm as it can incorporate existing black-box BO optimizers, such as BO, TuRBO (Eriksson et al., 2019), and BAxUS (Papenmeier et al., 2022), to find the global optimum of the objective function within our derived local regions. We evaluate our proposed method on various benchmark synthetic and real-world problems. The results demonstrate that our method outperforms existing state-of-the-art techniques.

Storing such a tensor often requires too much computational effort, and for large values of the dimension d, this is We develop a new method HTBB for the multidimensional completely impossible due to the so-called curse of dimensionality black-box approximation and gradientfree (the memory for storing data and the complexity optimization, which is based on the low-rank of working with it grows exponentially in d). To overcome hierarchical Tucker decomposition with the use it, various compression formats for multidimensional tensors of the MaxVol indices selection procedure. Numerical are proposed: Canonical Polyadic decomposition aka experiments for 14 complex model problems CANDECOMP/PARAFAC (CPD) (Harshman et al., 1970), demonstrate the robustness of the proposed Tucker decomposition (Tucker, 1966), Tensor Train (TT) method for dimensions up to 1000, while it shows decomposition (Oseledets, 2011), Hierarchical Tucker (HT) significantly more accurate results than classical decomposition (Hackbusch & Kühn, 2009; Ballani et al., gradient-free optimization methods, as well as 2013), and their various modifications. These approaches approximation and optimization methods based make it possible to approximately represent the tensor in on the popular tensor train decomposition, which a compact low-rank (i.e., low-parameter) format and then represents a simpler case of a tensor network.

There has been a long-standing and widespread belief that Bayesian Optimization (BO) with standard Gaussian process (GP), referred to as standard BO, is ineffective in high-dimensional optimization problems. This perception may partly stem from the intuition that GPs struggle with high-dimensional inputs for covariance modeling and function estimation. While these concerns seem reasonable, empirical evidence supporting this belief is lacking. In this paper, we systematically investigated BO with standard GP regression across a variety of synthetic and real-world benchmark problems for high-dimensional optimization. Surprisingly, the performance with standard GP consistently ranks among the best, often outperforming existing BO methods specifically designed for high-dimensional optimization by a large margin. Contrary to the stereotype, we found that standard GP can serve as a capable surrogate for learning high-dimensional target functions. Without strong structural assumptions, BO with standard GP not only excels in high-dimensional optimization but also proves robust in accommodating various structures within the target functions. Furthermore, with standard GP, achieving promising optimization performance is possible by only using maximum likelihood estimation, eliminating the need for expensive Markov-Chain Monte Carlo (MCMC) sampling that might be required by more complex surrogate models. We thus advocate for a re-evaluation and in-depth study of the potential of standard BO in addressing high-dimensional problems.

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of a family of $\ell_0$-regularized problems. An efficient primal-dual algorithm is developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.

Maximizing a target variable as an operational objective in a structured causal model is an important problem. Existing Causal Bayesian Optimization (CBO) methods either rely on hard interventions that alter the causal structure to maximize the reward; or introduce action nodes to endogenous variables so that the data generation mechanisms are adjusted to achieve the objective. In this paper, a novel method is introduced to learn the distribution of exogenous variables, which is typically ignored or marginalized through expectation by existing methods. Exogenous distribution learning improves the approximation accuracy of structured causal models in a surrogate model that is usually trained with limited observational data. Moreover, the learned exogenous distribution extends existing CBO to general causal schemes beyond Additive Noise Models (ANM). The recovery of exogenous variables allows us to use a more flexible prior for noise or unobserved hidden variables. A new CBO method is developed by leveraging the learned exogenous distribution. Experiments on different datasets and applications show the benefits of our proposed method.

The privacy in classical federated learning can be breached through the use of local gradient results along with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide more privacy. Additionally, sending an $N$ dimensional data vector through a quantum channel requires sending $\log N$ entangled qubits, which can potentially provide exponential efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model where fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the coming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model as a quantum state is fed into client-side chips directly; therefore, it does not require measurements on the upcoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over the models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values of these parameters.