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Stochastic gradient algorithms are widely used for both optimization and sampling in large-scale learning and inference problems. However, in practice, tuning these algorithms is typically done using heuristics and trial-and-error rather than rigorous, generalizable theory. To address this gap between theory and practice, we novel insights into the effect of tuning parameters by characterizing the large-sample behavior of iterates of a very general class of preconditioned stochastic gradient algorithms with fixed step size. In the optimization setting, our results show that iterate averaging with a large fixed step size can result in statistically efficient approximation of the (local) M-estimator. In the sampling context, our results show that with appropriate choices of tuning parameters, the limiting stationary covariance can match either the Bernstein--von Mises limit of the posterior, adjustments to the posterior for model misspecification, or the asymptotic distribution of the MLE; and that with a naive tuning the limit corresponds to none of these. Moreover, we argue that an essentially independent sample from the stationary distribution can be obtained after a fixed number of passes over the dataset. We validate our asymptotic results in realistic finite-sample regimes via several experiments using simulated and real data. Overall, we demonstrate that properly tuned stochastic gradient algorithms with constant step size offer a computationally efficient and statistically robust approach to obtaining point estimates or posterior-like samples.

We consider a causal inference model in which individuals interact in a social network and they may not comply with the assigned treatments. Estimating causal parameters is challenging in the presence of network interference of unknown form, as each individual may be influenced by both close individuals and distant ones in complex ways. Noncompliance with treatment assignment further complicates this problem, and prior methods dealing with network spillovers but disregarding the noncompliance issue may underestimate the effect of the treatment receipt on the outcome. To estimate meaningful causal parameters, we introduce a new concept of exposure mapping, which summarizes potentially complicated spillover effects into a fixed dimensional statistic of instrumental variables. We investigate identification conditions for the intention-to-treat effect and the average causal effect for compliers, while explicitly considering the possibility of misspecification of exposure mapping. Based on our identification results, we develop nonparametric estimation procedures via inverse probability weighting. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework, which is convenient for dealing with unknown forms of spillovers between individuals. For an empirical illustration, we apply our method to experimental data on the anti-conflict intervention school program.

We study \textit{rescaled gradient dynamical systems} in a Hilbert space $\mathcal{H}$, where implicit discretization in a finite-dimensional Euclidean space leads to high-order methods for solving monotone equations (MEs). Our framework can be interpreted as a natural generalization of celebrated dual extrapolation method~\citep{Nesterov-2007-Dual} from first order to high order via appeal to the regularization toolbox of optimization theory~\citep{Nesterov-2021-Implementable, Nesterov-2021-Inexact}. More specifically, we establish the existence and uniqueness of a global solution and analyze the convergence properties of solution trajectories. We also present discrete-time counterparts of our high-order continuous-time methods, and we show that the $p^{th}$-order method achieves an ergodic rate of $O(k^{-(p+1)/2})$ in terms of a restricted merit function and a pointwise rate of $O(k^{-p/2})$ in terms of a residue function. Under regularity conditions, the restarted version of $p^{th}$-order methods achieves local convergence with the order $p \geq 2$. Notably, our methods are \textit{optimal} since they have matched the lower bound established for solving the monotone equation problems under a standard linear span assumption~\citep{Lin-2022-Perseus}.

Clustering has received much attention in Statistics and Machine learning with the aim of developing statistical models and autonomous algorithms which are capable of acquiring information from raw data in order to perform exploratory analysis.Several techniques have been developed to cluster sampled univariate vectors only considering the average value over the whole period and as such they have not been able to explore fully the underlying distribution as well as other features of the data, especially in presence of structured time series. We propose a model-based clustering technique that is based on quantile regression permitting us to cluster bivariate time series at different quantile levels. We model the within cluster density using asymmetric Laplace distribution allowing us to take into account asymmetry in the distribution of the data. We evaluate the performance of the proposed technique through a simulation study. The method is then applied to cluster time series observed from Glob-colour satellite data related to trophic status indices with aim of evaluating their temporal dynamics in order to identify homogeneous areas, in terms of trophic status, in the Gulf of Gabes.

Harnessing parity-time (PT) symmetry with balanced gain and loss profiles has created a variety of opportunities in electronics from wireless energy transfer to telemetry sensing and topological defect engineering. However, existing implementations often employ ad-hoc approaches at low operating frequencies and are unable to accommodate large-scale integration. Here, we report a fully integrated realization of PT-symmetry in a standard complementary metal-oxide-semiconductor technology. Our work demonstrates salient PT-symmetry features such as phase transition as well as the ability to manipulate broadband microwave generation and propagation beyond the limitations encountered by exiting schemes. The system shows 2.1 times bandwidth and 30 percentage noise reduction compared to conventional microwave generation in oscillatory mode and displays large non-reciprocal microwave transport from 2.75 to 3.10 gigahertz in non-oscillatory mode due to enhanced nonlinearities. This approach could enrich integrated circuit (IC) design methodology beyond well-established performance limits and enable the use of scalable IC technology to study topological effects in high-dimensional non-Hermitian systems.

We are motivated by the problem of learning policies for robotic systems with rich sensory inputs (e.g., vision) in a manner that allows us to guarantee generalization to environments unseen during training. We provide a framework for providing such generalization guarantees by leveraging a finite dataset of real-world environments in combination with a (potentially inaccurate) generative model of environments. The key idea behind our approach is to utilize the generative model in order to implicitly specify a prior over policies. This prior is updated using the real-world dataset of environments by minimizing an upper bound on the expected cost across novel environments derived via Probably Approximately Correct (PAC)-Bayes generalization theory. We demonstrate our approach on two simulated systems with nonlinear/hybrid dynamics and rich sensing modalities: (i) quadrotor navigation with an onboard vision sensor, and (ii) grasping objects using a depth sensor. Comparisons with prior work demonstrate the ability of our approach to obtain stronger generalization guarantees by utilizing generative models. We also present hardware experiments for validating our bounds for the grasping task.

With the aid of hardware and software developments, there has been a surge of interests in solving partial differential equations by deep learning techniques, and the integration with domain decomposition strategies has recently attracted considerable attention due to its enhanced representation and parallelization capacity of the network solution. While there are already several works that substitute the numerical solver of overlapping Schwarz methods with the deep learning approach, the non-overlapping counterpart has not been thoroughly studied yet because of the inevitable interface overfitting problem that would propagate the errors to neighbouring subdomains and eventually hamper the convergence of outer iteration. In this work, a novel learning approach, i.e., the compensated deep Ritz method, is proposed to enable the flux transmission across subregion interfaces with guaranteed accuracy, thereby allowing us to construct effective learning algorithms for realizing the more general non-overlapping domain decomposition methods in the presence of overfitted interface conditions. Numerical experiments on a series of elliptic boundary value problems including the regular and irregular interfaces, low and high dimensions, smooth and high-contrast coefficients on multidomains are carried out to validate the effectiveness of our proposed domain decomposition learning algorithms.

Current rapid changes in climate increase the urgency to change energy production and consumption management, to reduce carbon and other green-house gas production. In this context, the French electricity network management company RTE (R{\'e}seau de Transport d'{\'E}lectricit{\'e}) has recently published the results of an extensive study outlining various scenarios for tomorrow's French power management. We propose a challenge that will test the viability of such a scenario. The goal is to control electricity transportation in power networks, while pursuing multiple objectives: balancing production and consumption, minimizing energetic losses, and keeping people and equipment safe and particularly avoiding catastrophic failures. While the importance of the application provides a goal in itself, this challenge also aims to push the state-of-the-art in a branch of Artificial Intelligence (AI) called Reinforcement Learning (RL), which offers new possibilities to tackle control problems. In particular, various aspects of the combination of Deep Learning and RL called Deep Reinforcement Learning remain to be harnessed in this application domain. This challenge belongs to a series started in 2019 under the name "Learning to run a power network" (L2RPN). In this new edition, we introduce new more realistic scenarios proposed by RTE to reach carbon neutrality by 2050, retiring fossil fuel electricity production, increasing proportions of renewable and nuclear energy and introducing batteries. Furthermore, we provide a baseline using state-of-the-art reinforcement learning algorithm to stimulate the future participants.

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a breadth of decisions in modern society. Using several classic examples from fisheries management, I demonstrate that selecting the model or models that produce the most accurate and precise forecast (measured by statistical scores) can sometimes lead to worse outcomes (measured by real-world objectives). This can create a forecast trap, in which the outcomes such as fish biomass or economic yield decline while the manager becomes increasingly convinced that these actions are consistent with the best models and data available. The forecast trap is not unique to this example, but a fundamental consequence of non-uniqueness of models. Existing practices promoting a broader set of models are the best way to avoid the trap.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.