Federated learning often suffers from unstable and slow convergence due to heterogeneous characteristics of participating clients. Such tendency is aggravated when the client participation ratio is low since the information collected from the clients at each round is prone to be more inconsistent. To tackle the challenge, we propose a novel federated learning framework, which improves the stability of the server-side aggregation step, which is achieved by sending the clients an accelerated model estimated with the global gradient to guide the local gradient updates. Our algorithm naturally aggregates and conveys the global update information to participants with no additional communication cost and does not require to store the past models in the clients. We also regularize local update to further reduce the bias and improve the stability of local updates. We perform comprehensive empirical studies on real data under various settings and demonstrate the remarkable performance of the proposed method in terms of accuracy and communication-efficiency compared to the state-of-the-art methods, especially with low client participation rates. Our code is available at https://github.com/ ninigapa0/FedAGM

Increasing complexity comes from some factors including uncertainty, ambiguity, inconsistency, multiple dimensionalities, increasing the number of effective factors and relation between them. Some of these features are common among most real-world problems which are considered complex and dynamic problems. In other words, since the data and relations in real world applications are usually highly complex and inaccurate, modeling real complex systems based on observed data is a challenging task especially for large scale, inaccurate and non stationary datasets. Therefore, to cover and address these difficulties, the existence of a computational system with the capability of extracting knowledge from the complex system with the ability to simulate its behavior is essential. In other words, it is needed to find a robust approach and solution to handle real complex problems in an easy and meaningful way [1]. Hard computing methods depend on quantitative values with expensive solutions and lack of ability to represent the problem in real life due to some uncertainties. In contrast, soft computing approaches act as alternative tools to deal with the reasoning of complex problems [2]. Using soft computing methods such as fuzzy logic, neural network, genetic algorithms or a combination of these allows achieving robustness, tractable and more practical solutions. Generally, two types of methods are used for analyzing and modeling dynamic systems including quantitative and qualitative approaches.

Meanwhile, applications of RL have only begun to expand beyond these constrained game environments to more diverse and complex real-world environments such as chip design [86], chemical reaction optimization [133] and performing long-term recommendations [45]. To further progress towards these more complex real-world environments, greater alleviation of challenges currently facing RL (e.g., generalization, robustness, scalability, and safety) is needed [7, 27, 72, 108]. Moreover, we can expect that as the complexity of environments increases, the difficulty in alleviating these challenges will increase as well [27]. For the purpose of this paper, we broadly define known RL challenges as either an aptitude or alignment problem. Aptitude encompasses challenges concerned with being able to learn. Aptitude includes ideas such as robustness, the ability of RL to perform a task (e.g., asymptotic performance) and generalize within/between environments of similar complexity; scalability, the ability of RL to scale up to more complex environment; and aptness, the rate at which a RL algorithm can learn to solve a problem or achieve a desired performance level. Likewise, alignment encompasses challenges concerned with learning as intended [7, 27, 72]. The hypothetical paperclip agent [18] is a classic example of misalignment.

We study generalization bounds for noisy stochastic mini-batch iterative algorithms based on the notion of stability. Recent years have seen key advances in data-dependent generalization bounds for noisy iterative learning algorithms such as stochastic gradient Langevin dynamics (SGLD) based on stability (Mou et al., 2018; Li et al., 2020) and information theoretic approaches (Xu and Raginsky, 2017; Negrea et al., 2019; Steinke and Zakynthinou, 2020; Haghifam et al., 2020). In this paper, we unify and substantially generalize stability based generalization bounds and make three technical advances. First, we bound the generalization error of general noisy stochastic iterative algorithms (not necessarily gradient descent) in terms of expected (not uniform) stability. The expected stability can in turn be bounded by a Le Cam Style Divergence. Such bounds have a O(1/n) sample dependence unlike many existing bounds with O(1/\sqrt{n}) dependence. Second, we introduce Exponential Family Langevin Dynamics(EFLD) which is a substantial generalization of SGLD and which allows exponential family noise to be used with stochastic gradient descent (SGD). We establish data-dependent expected stability based generalization bounds for general EFLD algorithms. Third, we consider an important special case of EFLD: noisy sign-SGD, which extends sign-SGD using Bernoulli noise over {-1,+1}. Generalization bounds for noisy sign-SGD are implied by that of EFLD and we also establish optimization guarantees for the algorithm. Further, we present empirical results on benchmark datasets to illustrate that our bounds are non-vacuous and quantitatively much sharper than existing bounds.

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.

We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the system's expected performance. An SBOS problem compares different systems based on their expected performances under their own optimally chosen decision to select the best, without advance knowledge of expected performances of the systems nor the optimizing decision inside each system. We design easy-to-implement algorithms that adaptively chooses a system and a choice of decision to evaluate the noisy system performance, sequentially eliminates inferior systems, and eventually recommends a system as the best after spending a user-specified budget. The proposed algorithms integrate the stochastic gradient descent method and the sequential elimination method to simultaneously exploit the structure inside each system and make comparisons across systems. For the proposed algorithms, we prove exponential rates of convergence to zero for the probability of false selection, as the budget grows to infinity. We conduct three numerical examples that represent three practical cases of SBOS problems. Our proposed algorithms demonstrate consistent and stronger performances in terms of the probability of false selection over benchmark algorithms under a range of problem settings and sampling budgets.

Linear and Quadratic Discriminant Analysis are well-known The new method called Generalized QDA (GQDA) classical methods but can heavily suffer from non-Gaussian relies on the estimation of a threshold parameter, whose optimal distributions and/or contaminated datasets, mainly because of value is fixed for each sub-family of distribution. The the underlying Gaussian assumption that is not robust. To fill case c 1 corresponds to the Gaussian case. Finally, [10] improved this gap, this paper presents a new robust discriminant analysis the previous work by adding robust estimators, coming where each data point is drawn by its own arbitrary Elliptically up with the Robust GQDA (RGQDA) method. Symmetrical (ES) distribution and its own arbitrary All these methods assume that all clusters belong to the scale parameter. Such a model allows for possibly very heterogeneous, same distribution family. In practice, such an hypothesis may independent but non-identically distributed samples.

Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification.

We propose an information-theoretic bias measurement technique through a causal interpretation of spurious correlation, which is effective to identify the feature-level algorithmic bias by taking advantage of conditional mutual information. Although several bias measurement methods have been proposed and widely investigated to achieve algorithmic fairness in various tasks such as face recognition, their accuracy- or logit-based metrics are susceptible to leading to trivial prediction score adjustment rather than fundamental bias reduction. Hence, we design a novel debiasing framework against the algorithmic bias, which incorporates a bias regularization loss derived by the proposed information-theoretic bias measurement approach. In addition, we present a simple yet effective unsupervised debiasing technique based on stochastic label noise, which does not require the explicit supervision of bias information. The proposed bias measurement and debiasing approaches are validated in diverse realistic scenarios through extensive experiments on multiple standard benchmarks.

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