By enabling agents to communicate, recent cooperative multi-agent reinforcement learning (MARL) methods have demonstrated better task performance and more coordinated behavior. Most existing approaches facilitate inter-agent communication by allowing agents to send messages to each other through free communication channels, i.e., cheap talk channels. Current methods require these channels to be constantly accessible and known to the agents a priori. In this work, we lift these requirements such that the agents must discover the cheap talk channels and learn how to use them. Hence, the problem has two main parts: cheap talk discovery (CTD) and cheap talk utilization (CTU). We introduce a novel conceptual framework for both parts and develop a new algorithm based on mutual information maximization that outperforms existing algorithms in CTD/CTU settings. We also release a novel benchmark suite to stimulate future research in CTD/CTU.

The slowing down of Moore's law has driven the development of unconventional computing paradigms, such as specialized Ising machines tailored to solve combinatorial optimization problems. In this paper, we show a new application domain for probabilistic bit (p-bit) based Ising machines by training deep generative AI models with them. Using sparse, asynchronous, and massively parallel Ising machines we train deep Boltzmann networks in a hybrid probabilistic-classical computing setup. We use the full MNIST dataset without any downsampling or reduction in hardware-aware network topologies implemented in moderately sized Field Programmable Gate Arrays (FPGA). Our machine, which uses only 4,264 nodes (p-bits) and about 30,000 parameters, achieves the same classification accuracy (90%) as an optimized software-based restricted Boltzmann Machine (RBM) with approximately 3.25 million parameters. Additionally, the sparse deep Boltzmann network can generate new handwritten digits, a task the 3.25 million parameter RBM fails at despite achieving the same accuracy. Our hybrid computer takes a measured 50 to 64 billion probabilistic flips per second, which is at least an order of magnitude faster than superficially similar Graphics and Tensor Processing Unit (GPU/TPU) based implementations. The massively parallel architecture can comfortably perform the contrastive divergence algorithm (CD-n) with up to n = 10 million sweeps per update, beyond the capabilities of existing software implementations. These results demonstrate the potential of using Ising machines for traditionally hard-to-train deep generative Boltzmann networks, with further possible improvement in nanodevice-based realizations.

Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process (LVGP) overcomes this issue by first mapping each qualitative factor to underlying latent variables (LVs), and then uses any standard GP covariance function over these LVs. The LVs are estimated similarly to the other GP hyperparameters through maximum likelihood estimation, and then plugged into the prediction expressions. However, this plug-in approach will not account for uncertainty in estimation of the LVs, which can be significant especially with limited training data. In this work, we develop a fully Bayesian approach for the LVGP model and for visualizing the effects of the qualitative inputs via their LVs. We also develop approximations for scaling up LVGPs and fully Bayesian inference for the LVGP hyperparameters. We conduct numerical studies comparing plug-in inference against fully Bayesian inference over a few engineering models and material design applications. In contrast to previous studies on standard GP modeling that have largely concluded that a fully Bayesian treatment offers limited improvements, our results show that for LVGP modeling it offers significant improvements in prediction accuracy and uncertainty quantification over the plug-in approach.

Recently, mean field control (MFC) has provided a tractable and theoretically founded approach to otherwise difficult cooperative multi-agent control. However, the strict assumption of many independent, homogeneous agents may be too stringent in practice. In this work, we propose a novel discrete-time generalization of Markov decision processes and MFC to both many minor agents and potentially complex major agents -- major-minor mean field control (M3FC). In contrast to deterministic MFC, M3FC allows for stochastic minor agent distributions with strong correlation between minor agents through the major agent state, which can model arbitrary problem details not bound to any agent. Theoretically, we give rigorous approximation properties with novel proofs for both M3FC and existing MFC models in the finite multi-agent problem, together with a dynamic programming principle for solving such problems. In the infinite-horizon discounted case, existence of an optimal stationary policy follows. Algorithmically, we propose the major-minor mean field proximal policy optimization algorithm (M3FPPO) as a novel multi-agent reinforcement learning algorithm and demonstrate its success in illustrative M3FC-type problems.

This type of data is commonly encountered in many fields, including economy (Bugni et al. (2009)), computational biology (Giacofci et al. (2013)) or environmental sciences (Bouveyron et al. (2021a)), to name a few. For an in-depth review of techniques and applications, we refer the interested readers to the books of Ferraty and Vieu (2006) and Ramsay and Silverman (2002, 2005). In many of these applications, such as electricity load, used for illustration here, we observe multiple curves corresponding to several individuals over a given time interval. As a result, one can expect a high heterogeneity of the data, both at the level of the studied individuals, that may correspond to different behavior or consumer profiles, but also on the time dimension where changes of power consumption regimes are likely to occur over the course of one year for instance. To consider a parametric model, homogeneous data is required, both at population and time levels.

The Variational Monte Carlo (VMC) is a promising approach for computing the ground state energy of many-body quantum problems and attracts more and more interests due to the development of machine learning. The recent paradigms in VMC construct neural networks as trial wave functions, sample quantum configurations using Markov chain Monte Carlo (MCMC) and train neural networks with stochastic gradient descent (SGD) method. However, the theoretical convergence of VMC is still unknown when SGD interacts with MCMC sampling given a well-designed trial wave function. Since MCMC reduces the difficulty of estimating gradients, it has inevitable bias in practice. Moreover, the local energy may be unbounded, which makes it harder to analyze the error of MCMC sampling. Therefore, we assume that the local energy is sub-exponential and use the Bernstein inequality for non-stationary Markov chains to derive error bounds of the MCMC estimator. Consequently, VMC is proven to have a first order convergence rate $O(\log K/\sqrt{n K})$ with $K$ iterations and a sample size $n$. It partially explains how MCMC influences the behavior of SGD. Furthermore, we verify the so-called correlated negative curvature condition and relate it to the zero-variance phenomena in solving eigenvalue functions. It is shown that VMC escapes from saddle points and reaches $(\epsilon,\epsilon^{1/4})$ -approximate second order stationary points or $\epsilon^{1/2}$-variance points in at least $O(\epsilon^{-11/2}\log^{2}(1/\epsilon) )$ steps with high probability. Our analysis enriches the understanding of how VMC converges efficiently and can be applied to general variational methods in physics and statistics.

In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples and computation. In recent years, researchers have introduced objectives and corresponding reinforcement-learning algorithms beyond the classic cumulative rewards, such as objectives specified as linear temporal logic formulas. However, questions about the PAC-learnability of these new objectives have remained open. This work demonstrates the PAC-learnability of general reinforcement-learning objectives through sufficient conditions for PAC-learnability in two analysis settings. In particular, for the analysis that considers only sample complexity, we prove that if an objective given as an oracle is uniformly continuous, then it is PAC-learnable. Further, for the analysis that considers computational complexity, we prove that if an objective is computable, then it is PAC-learnable. In other words, if a procedure computes successive approximations of the objective's value, then the objective is PAC-learnable. We give three applications of our condition on objectives from the literature with previously unknown PAC-learnability and prove that these objectives are PAC-learnable. Overall, our result helps verify existing objectives' PAC-learnability. Also, as some studied objectives that are not uniformly continuous have been shown to be not PAC-learnable, our results could guide the design of new PAC-learnable objectives.

Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to geoscience and climate systems. Recently, much effort has been given in combining DA, UQ and machine learning (ML) techniques. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide. This paper provides the first overview of the state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. This review aims at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems. Therefore, this article has a special focus on how ML methods can overcome the existing limits of DA and UQ, and vice versa. Some exciting perspectives of this rapidly developing research field are also discussed.

The interaction and collaboration between humans and multiple robots represent a novel field of research known as human multi-robot systems. Adequately designed systems within this field allow teams composed of both humans and robots to work together effectively on tasks such as monitoring, exploration, and search and rescue operations. This paper presents a deep reinforcement learning-based affective workload allocation controller specifically for multi-human multi-robot teams. The proposed controller can dynamically reallocate workloads based on the performance of the operators during collaborative missions with multi-robot systems. The operators' performances are evaluated through the scores of a self-reported questionnaire (i.e., subjective measurement) and the results of a deep learning-based cognitive workload prediction algorithm that uses physiological and behavioral data (i.e., objective measurement). To evaluate the effectiveness of the proposed controller, we use a multi-human multi-robot CCTV monitoring task as an example and carry out comprehensive real-world experiments with 32 human subjects for both quantitative measurement and qualitative analysis. Our results demonstrate the performance and effectiveness of the proposed controller and highlight the importance of incorporating both subjective and objective measurements of the operators' cognitive workload as well as seeking consent for workload transitions, to enhance the performance of multi-human multi-robot teams.

Data-driven algorithms are only as good as the data they work with, while data sets, especially social data, often fail to represent minorities adequately. Representation Bias in data can happen due to various reasons ranging from historical discrimination to selection and sampling biases in the data acquisition and preparation methods. Given that "bias in, bias out", one cannot expect AI-based solutions to have equitable outcomes for societal applications, without addressing issues such as representation bias. While there has been extensive study of fairness in machine learning models, including several review papers, bias in the data has been less studied. This paper reviews the literature on identifying and resolving representation bias as a feature of a data set, independent of how consumed later. The scope of this survey is bounded to structured (tabular) and unstructured (e.g., image, text, graph) data. It presents taxonomies to categorize the studied techniques based on multiple design dimensions and provides a side-by-side comparison of their properties. There is still a long way to fully address representation bias issues in data. The authors hope that this survey motivates researchers to approach these challenges in the future by observing existing work within their respective domains.