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Information about action costs is critical for real-world AI planning applications. Rather than rely solely on declarative action models, recent approaches also use black-box external action cost estimators, often learned from data, that are applied during the planning phase. These, however, can be computationally expensive, and produce uncertain values. In this paper we suggest a generalization of deterministic planning with action costs that allows selecting between multiple estimators for action cost, to balance computation time against bounded estimation uncertainty. This enables a much richer -- and correspondingly more realistic -- problem representation. Importantly, it allows planners to bound plan accuracy, thereby increasing reliability, while reducing unnecessary computational burden, which is critical for scaling to large problems. We introduce a search algorithm, generalizing $A^*$, that solves such planning problems, and additional algorithmic extensions. In addition to theoretical guarantees, extensive experiments show considerable savings in runtime compared to alternatives.

Continuous-time nonlinear optimal control problems hold great promise in real-world applications. After decades of development, reinforcement learning (RL) has achieved some of the greatest successes as a general nonlinear control design method. However, a recent comprehensive analysis of state-of-the-art continuous-time RL (CT-RL) methods, namely, adaptive dynamic programming (ADP)-based CT-RL algorithms, reveals they face significant design challenges due to their complexity, numerical conditioning, and dimensional scaling issues. Despite advanced theoretical results, existing ADP CT-RL synthesis methods are inadequate in solving even small, academic problems. The goal of this work is thus to introduce a suite of new CT-RL algorithms for control of affine nonlinear systems. Our design approach relies on two important factors. First, our methods are applicable to physical systems that can be partitioned into smaller subproblems. This constructive consideration results in reduced dimensionality and greatly improved intuitiveness of design. Second, we introduce a new excitation framework to improve persistence of excitation (PE) and numerical conditioning performance via classical input/output insights. Such a design-centric approach is the first of its kind in the ADP CT-RL community. In this paper, we progressively introduce a suite of (decentralized) excitable integral reinforcement learning (EIRL) algorithms. We provide convergence and closed-loop stability guarantees, and we demonstrate these guarantees on a significant application problem of controlling an unstable, nonminimum phase hypersonic vehicle (HSV).

Let $\Omega = [0,1]^d$ be the unit cube in $\mathbb{R}^d$. We study the problem of how efficiently, in terms of the number of parameters, deep neural networks with the ReLU activation function can approximate functions in the Sobolev spaces $W^s(L_q(\Omega))$ and Besov spaces $B^s_r(L_q(\Omega))$, with error measured in the $L_p(\Omega)$ norm. This problem is important when studying the application of neural networks in a variety of fields, including scientific computing and signal processing, and has previously been completely solved only when $p=q=\infty$. Our contribution is to provide a complete solution for all $1\leq p,q\leq \infty$ and $s > 0$, including asymptotically matching upper and lower bounds. The key technical tool is a novel bit-extraction technique which gives an optimal encoding of sparse vectors. This enables us to obtain sharp upper bounds in the non-linear regime where $p > q$. We also provide a novel method for deriving $L_p$-approximation lower bounds based upon VC-dimension when $p < \infty$. Our results show that very deep ReLU networks significantly outperform classical methods of approximation in terms of the number of parameters, but that this comes at the cost of parameters which are not encodable.

Two widely considered decentralized learning algorithms are Gossip and random walk-based learning. Gossip algorithms (both synchronous and asynchronous versions) suffer from high communication cost, while random-walk based learning experiences increased convergence time. In this paper, we design a fast and communication-efficient asynchronous decentralized learning mechanism DIGEST by taking advantage of both Gossip and random-walk ideas, and focusing on stochastic gradient descent (SGD). DIGEST is an asynchronous decentralized algorithm building on local-SGD algorithms, which are originally designed for communication efficient centralized learning. We design both single-stream and multi-stream DIGEST, where the communication overhead may increase when the number of streams increases, and there is a convergence and communication overhead trade-off which can be leveraged. We analyze the convergence of single- and multi-stream DIGEST, and prove that both algorithms approach to the optimal solution asymptotically for both iid and non-iid data distributions. We evaluate the performance of single- and multi-stream DIGEST for logistic regression and a deep neural network ResNet20. The simulation results confirm that multi-stream DIGEST has nice convergence properties; i.e., its convergence time is better than or comparable to the baselines in iid setting, and outperforms the baselines in non-iid setting.

In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.

Federated learning (FL) as distributed machine learning has gained popularity as privacy-aware Machine Learning (ML) systems have emerged as a technique that prevents privacy leakage by building a global model and by conducting individualized training of decentralized edge clients on their own private data. The existing works, however, employ privacy mechanisms such as Secure Multiparty Computing (SMC), Differential Privacy (DP), etc. Which are immensely susceptible to interference, massive computational overhead, low accuracy, etc. With the increasingly broad deployment of FL systems, it is challenging to ensure fairness and maintain active client participation in FL systems. Very few works ensure reasonably satisfactory performances for the numerous diverse clients and fail to prevent potential bias against particular demographics in FL systems. The current efforts fail to strike a compromise between privacy, fairness, and model performance in FL systems and are vulnerable to a number of additional problems. In this paper, we provide a comprehensive survey stating the basic concepts of FL, the existing privacy challenges, techniques, and relevant works concerning privacy in FL. We also provide an extensive overview of the increasing fairness challenges, existing fairness notions, and the limited works that attempt both privacy and fairness in FL. By comprehensively describing the existing FL systems, we present the potential future directions pertaining to the challenges of privacy-preserving and fairness-aware FL systems.

Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.

Federated Learning (FL) emerges as a distributed machine learning paradigm without end-user data transmission, effectively avoiding privacy leakage. Participating devices in FL are usually bandwidth-constrained, and the uplink is much slower than the downlink in wireless networks, which causes a severe uplink communication bottleneck. A prominent direction to alleviate this problem is federated dropout, which drops fractional weights of local models. However, existing federated dropout studies focus on random or ordered dropout and lack theoretical support, resulting in unguaranteed performance. In this paper, we propose Federated learning with Bayesian Inference-based Adaptive Dropout (FedBIAD), which regards weight rows of local models as probability distributions and adaptively drops partial weight rows based on importance indicators correlated with the trend of local training loss. By applying FedBIAD, each client adaptively selects a high-quality dropping pattern with accurate approximations and only transmits parameters of non-dropped weight rows to mitigate uplink costs while improving accuracy. Theoretical analysis demonstrates that the convergence rate of the average generalization error of FedBIAD is minimax optimal up to a squared logarithmic factor. Extensive experiments on image classification and next-word prediction show that compared with status quo approaches, FedBIAD provides 2x uplink reduction with an accuracy increase of up to 2.41% even on non-Independent and Identically Distributed (non-IID) data, which brings up to 72% decrease in training time.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.