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This work focuses on decentralized stochastic optimization in the presence of Byzantine attacks. During the optimization process, an unknown number of malfunctioning or malicious nodes, which we term as Byzantine workers, disobey the algorithmic protocol and send wrong messages to their neighbors. Even though various Byzantine-resilient algorithms have been developed for distributed stochastic optimization, we show that there are still two major challenges during the designation of robust aggregation rules suitable for decentralized stochastic optimization: disagreement and non-doubly stochastic mixing matrix. This paper provides a comprehensive analysis disclosing the negative effects of these two issues, and gives guidelines of designing favorable Byzantine-resilient decentralized stochastic optimization algorithms. Following the guidelines, we propose an iterative filtering-based robust aggregation rule termed iterative outlier scissor (IOS), which has provable Byzantine-resilience. Numerical experiments demonstrate the effectiveness of IOS.

Blockchain has recently attracted the attention of the industry due, in part, to its ability to automate asset transfers. It requires distributed participants to reach a consensus on a block despite the presence of malicious (a.k.a. Byzantine) participants. Malicious participants exploit regularly weaknesses of these blockchain consensus algorithms, with sometimes devastating consequences. In fact, these weaknesses are quite common and are well illustrated by the flaws in the hand-written proofs of existing blockchain consensus protocols [63]. Paradoxically, until now, no blockchain consensus has been holistically verified using model checking. In this paper, we remedy this paradox by model checking for the first time a blockchain consensus used in industry. We propose a holistic approach to verify the consensus algorithm of the Red Belly Blockchain [20], for any number $n$ of processes and any number $f<n/3$ of Byzantine processes. We decompose directly the algorithm pseudocode in two parts -- an inner broadcast algorithm and an outer decision algorithm -- each modelled as a threshold automaton [36], and we formalize their expected properties in linear-time temporal logic. We then automatically check the inner broadcasting algorithm, under a carefully identified fairness assumption. For the verification of the outer algorithm, we simplify the model of the inner algorithm by relying on its checked properties. Doing so, we formally verify not only the safety properties of the Red Belly Blockchain consensus but also its liveness in about 70 seconds.

We present a thorough study of the theoretical properties and devise efficient algorithms for the \emph{persistent Laplacian}, an extension of the standard combinatorial Laplacian to the setting of pairs (or, in more generality, sequences) of simplicial complexes $K \hookrightarrow L$, which was independently introduced by Lieutier et al. and by Wang et al. In particular, in analogy with the non-persistent case, we first prove that the nullity of the $q$-th persistent Laplacian $\Delta_q^{K,L}$ equals the $q$-th persistent Betti number of the inclusion $(K \hookrightarrow L)$. We then present an initial algorithm for finding a matrix representation of $\Delta_q^{K,L}$, which itself helps interpret the persistent Laplacian. We exhibit a novel relationship between the persistent Laplacian and the notion of Schur complement of a matrix which has several important implications. In the graph case, it both uncovers a link with the notion of effective resistance and leads to a persistent version of the Cheeger inequality. This relationship also yields an additional, very simple algorithm for finding (a matrix representation of) the $q$-th persistent Laplacian which in turn leads to a novel and fundamentally different algorithm for computing the $q$-th persistent Betti number for a pair $(K,L)$ which can be significantly more efficient than standard algorithms. Finally, we study persistent Laplacians for simplicial filtrations and present novel stability results for their eigenvalues. Our work brings methods from spectral graph theory, circuit theory, and persistent homology together with a topological view of the combinatorial Laplacian on simplicial complexes.

The next generation of networks will actively embrace artificial intelligence (AI) and machine learning (ML) technologies for automation networks and optimal network operation strategies. The emerging network structure represented by Open RAN (O-RAN) conforms to this trend, and the radio intelligent controller (RIC) at the centre of its specification serves as an ML applications host. Various ML models, especially Reinforcement Learning (RL) models, are regarded as the key to solving RAN-related multi-objective optimization problems. However, it should be recognized that most of the current RL successes are confined to abstract and simplified simulation environments, which may not directly translate to high performance in complex real environments. One of the main reasons is the modelling gap between the simulation and the real environment, which could make the RL agent trained by simulation ill-equipped for the real environment. This issue is termed as the sim2real gap. This article brings to the fore the sim2real challenge within the context of O-RAN. Specifically, it emphasizes the characteristics, and benefits that the digital twins (DT) could have as a place for model development and verification. Several use cases are presented to exemplify and demonstrate failure modes of the simulations trained RL model in real environments. The effectiveness of DT in assisting the development of RL algorithms is discussed. Then the current state of the art learning-based methods commonly used to overcome the sim2real challenge are presented. Finally, the development and deployment concerns for the RL applications realisation in O-RAN are discussed from the view of the potential issues like data interaction, environment bottlenecks, and algorithm design.

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating distribution. Under the weaker and distribution dependent notions of stability such as hypothesis stability and $L_2$-stability, the literature suggests that only polynomial generalization bounds are possible in general cases. The present paper addresses this long standing tension between these two regimes of results and makes progress towards relaxing it inside a classic framework of confidence-boosting. To this end, we first establish an in-expectation first moment generalization error bound for potentially randomized learning algorithms with $L_2$-stability, based on which we then show that a properly designed subbagging process leads to near-tight exponential generalization bounds over the randomness of both data and algorithm. We further substantialize these generic results to stochastic gradient descent (SGD) to derive improved high-probability generalization bounds for convex or non-convex optimization problems with natural time decaying learning rates, which have not been possible to prove with the existing hypothesis stability or uniform stability based results.

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the sample is drawn i.i.d. from the input distribution, the least squares solution for that sample can be viewed as the natural estimator of the optimum. Unfortunately, this estimator almost always incurs an undesirable bias coming from the randomness of the input points, which is a significant bottleneck in model averaging. In this paper we show that it is possible to draw a non-i.i.d. sample of input points such that, regardless of the response model, the least squares solution is an unbiased estimator of the optimum. Moreover, this sample can be produced efficiently by augmenting a previously drawn i.i.d. sample with an additional set of $d$ points, drawn jointly according to a certain determinantal point process constructed from the input distribution rescaled by the squared volume spanned by the points. Motivated by this, we develop a theoretical framework for studying volume-rescaled sampling, and in the process prove a number of new matrix expectation identities. We use them to show that for any input distribution and $\epsilon>0$ there is a random design consisting of $O(d\log d+ d/\epsilon)$ points from which an unbiased estimator can be constructed whose expected square loss over the entire distribution is bounded by $1+\epsilon$ times the loss of the optimum. We provide efficient algorithms for generating such unbiased estimators in a number of practical settings and support our claims experimentally.

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex optimization framework, where (one pass, without-replacement) SGD is classically known to minimize the population risk at rate $O(1/\sqrt n)$, and prove that, surprisingly, there exist problem instances where the SGD solution exhibits both empirical risk and generalization gap of $\Omega(1)$. Consequently, it turns out that SGD is not algorithmically stable in any sense, and its generalization ability cannot be explained by uniform convergence or any other currently known generalization bound technique for that matter (other than that of its classical analysis). We then continue to analyze the closely related with-replacement SGD, for which we show that an analogous phenomenon does not occur and prove that its population risk does in fact converge at the optimal rate. Finally, we interpret our main results in the context of without-replacement SGD for finite-sum convex optimization problems, and derive upper and lower bounds for the multi-epoch regime that significantly improve upon previously known results.

Much of the literature on optimal design of bandit algorithms is based on minimization of expected regret. It is well known that designs that are optimal over certain exponential families can achieve expected regret that grows logarithmically in the number of arm plays, at a rate governed by the Lai-Robbins lower bound. In this paper, we show that when one uses such optimized designs, the regret distribution of the associated algorithms necessarily has a very heavy tail, specifically, that of a truncated Cauchy distribution. Furthermore, for $p>1$, the $p$'th moment of the regret distribution grows much faster than poly-logarithmically, in particular as a power of the total number of arm plays. We show that optimized UCB bandit designs are also fragile in an additional sense, namely when the problem is even slightly mis-specified, the regret can grow much faster than the conventional theory suggests. Our arguments are based on standard change-of-measure ideas, and indicate that the most likely way that regret becomes larger than expected is when the optimal arm returns below-average rewards in the first few arm plays, thereby causing the algorithm to believe that the arm is sub-optimal. To alleviate the fragility issues exposed, we show that UCB algorithms can be modified so as to ensure a desired degree of robustness to mis-specification. In doing so, we also provide a sharp trade-off between the amount of UCB exploration and the tail exponent of the resulting regret distribution.

We design simple and optimal policies that ensure safety against heavy-tailed risk in the classical multi-armed bandit problem. We start by showing that some widely used policies such as the standard Upper Confidence Bound policy and the Thompson Sampling policy incur heavy-tailed risk; that is, the worst-case probability of incurring a linear regret slowly decays at a polynomial rate of $1/T$, where $T$ is the time horizon. We further show that this heavy-tailed risk exists for all "instance-dependent consistent" policies. To ensure safety against such heavy-tailed risk, for the two-armed bandit setting, we provide a simple policy design that (i) has the worst-case optimality for the expected regret at order $\tilde O(\sqrt{T})$ and (ii) has the worst-case tail probability of incurring a linear regret decay at an exponential rate $\exp(-\Omega(\sqrt{T}))$. We further prove that this exponential decaying rate of the tail probability is optimal across all policies that have worst-case optimality for the expected regret. Finally, we improve the policy design and analysis to the general $K$-armed bandit setting. We provide detailed characterization of the tail probability bound for any regret threshold under our policy design. Namely, the worst-case probability of incurring a regret larger than $x$ is upper bounded by $\exp(-\Omega(x/\sqrt{KT}))$. Numerical experiments are conducted to illustrate the theoretical findings. Our results reveal insights on the incompatibility between consistency and light-tailed risk, whereas indicate that worst-case optimality on expected regret and light-tailed risk are compatible.

Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.