Federated learning is a new distributed machine learning framework, where a bunch of heterogeneous clients collaboratively train a model without sharing training data. In this work, we consider a practical and ubiquitous issue in federated learning: intermittent client availability, where the set of eligible clients may change during the training process. Such an intermittent client availability model would significantly deteriorate the performance of the classical Federated Averaging algorithm (FedAvg for short). We propose a simple distributed non-convex optimization algorithm, called Federated Latest Averaging (FedLaAvg for short), which leverages the latest gradients of all clients, even when the clients are not available, to jointly update the global model in each iteration. Our theoretical analysis shows that FedLaAvg attains the convergence rate of $O(1/(N^{1/4} T^{1/2}))$, achieving a sublinear speedup with respect to the total number of clients. We implement and evaluate FedLaAvg with the CIFAR-10 dataset. The evaluation results demonstrate that FedLaAvg indeed reaches a sublinear speedup and achieves 4.23% higher test accuracy than FedAvg.

Recent years have seen an increasing integration of distributed renewable energy resources into existing electric power grids. Due to the uncertain nature of renewable energy resources, network operators are faced with new challenges in balancing load and generation. In order to meet the new requirements, intelligent distributed energy resource plants can be used. However, the calculation of an adequate schedule for the unit commitment of such distributed energy resources is a complex optimization problem which is typically too complex for standard optimization algorithms if large numbers of distributed energy resources are considered. For solving such complex optimization tasks, population-based metaheuristics -- as, e.g., evolutionary algorithms -- represent powerful alternatives. Admittedly, evolutionary algorithms do require lots of computational power for solving such problems in a timely manner. One promising solution for this performance problem is the parallelization of the usually time-consuming evaluation of alternative solutions. In the present paper, a new generic and highly scalable parallel method for unit commitment of distributed energy resources using metaheuristic algorithms is presented. It is based on microservices, container virtualization and the publish/subscribe messaging paradigm for scheduling distributed energy resources. Scalability and applicability of the proposed solution are evaluated by performing parallelized optimizations in a big data environment for three distinct distributed energy resource scheduling scenarios. Thereby, unlike all other optimization methods in the literature, the new method provides cluster or cloud parallelizability and is able to deal with a comparably large number of distributed energy resources. The application of the new proposed method results in very good performance for scaling up optimization speed.

In this work we present a new method of black-box optimization and constraint satisfaction. Existing algorithms that have attempted to solve this problem are unable to consider multiple modes, and are not able to adapt to changes in environment dynamics. To address these issues, we developed a modified Cross-Entropy Method (CEM) that uses a masked auto-regressive neural network for modeling uniform distributions over the solution space. We train the model using maximum entropy policy gradient methods from Reinforcement Learning. Our algorithm is able to express complicated solution spaces, thus allowing it to track a variety of different solution regions. We empirically compare our algorithm with variations of CEM, including one with a Gaussian prior with fixed variance, and demonstrate better performance in terms of: number of diverse solutions, better mode discovery in multi-modal problems, and better sample efficiency in certain cases.

Area under ROC curve (AUC) is a widely used performance measure for classification models. We propose a new distributionally robust AUC maximization model (DR-AUC) that relies on the Kantorovich metric and approximates the AUC with the hinge loss function. We use duality theory to reformulate the DR-AUC model as a tractable convex quadratic optimization problem. The numerical experiments show that the proposed DR-AUC model -- benchmarked with the standard deterministic AUC and the support vector machine models - improves the out-of-sample performance over the majority of the considered datasets. The results are particularly encouraging since our numerical experiments are conducted with training sets of small size which have been known to be conducive to low out-of-sample performance.

We develop two new stochastic Gauss-Newton algorithms for solving a class of stochastic nonconvex compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions. We use both classical stochastic and SARAH estimators for approximating function values and Jacobians. In the expectation case, we establish $\mathcal{O}(\varepsilon^{-2})$ iteration complexity to achieve a stationary point in expectation and estimate the total number of stochastic oracle calls for both function values and its Jacobian, where $\varepsilon$ is a desired accuracy. In the finite sum case, we also estimate the same iteration complexity and the total oracle calls with high probability. To our best knowledge, this is the first time such global stochastic oracle complexity is established for stochastic Gauss-Newton methods. We illustrate our theoretical results via numerical examples on both synthetic and real datasets.

We consider combinatorial semi-bandits over a set of arms ${\cal X} \subset \{0,1\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\cal O}\Big( {d (\ln m)^2 (\ln T) \over \Delta_{\min} }\Big)$, but it has computational complexity ${\cal O}(|{\cal X}|)$ which is typically exponential in $d$, and cannot be used in large dimensions. We propose the first algorithm which is both computationally and statistically efficient for this problem with regret $R(T) = {\cal O} \Big({d (\ln m)^2 (\ln T)\over \Delta_{\min} }\Big)$ and computational complexity ${\cal O}(T {\bf poly}(d))$. Our approach involves carefully designing an approximate version of ESCB with the same regret guarantees, showing that this approximate algorithm can be implemented in time ${\cal O}(T {\bf poly}(d))$ by repeatedly maximizing a linear function over ${\cal X}$ subject to a linear budget constraint, and showing how to solve this maximization problems efficiently.

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization that employ sampling and sketching of the Hessian. Existing works do not take the bias of the estimators into consideration, which limits their application to massively parallel computation. We provide closed-form formulas for regularization parameters and step sizes that provably minimize the bias for sketched Newton directions. We also extend the framework of second order averaging methods to introduce an unbiased distributed optimization framework for heterogeneous computing systems with varying worker resources. Additionally, we demonstrate the implications of our theoretical findings via large scale experiments performed on a serverless computing platform.

Machine learning is increasingly being used in various applications that make decisions for individuals. For such applications, we need to strike a balance between achieving good prediction accuracy and making fair decisions with respect to a sensitive feature (e.g., race or gender), which is difficult in complex real-world scenarios. Existing methods measure the unfairness in such scenarios as {\it unfair causal effects} and constrain its mean to zero. Unfortunately, with these methods, the decisions are not necessarily fair for all individuals because even when the mean unfair effect is zero, unfair effects might be positive for some individuals and negative for others, which is discriminatory for them. To learn a classifier that is fair for all individuals, we define unfairness as the {\it probability of individual unfairness} (PIU) and propose to solve an optimization problem that constrains an upper bound on PIU. We theoretically illustrate why our method achieves individual fairness. Experimental results demonstrate that our method learns an individually fair classifier at a slight cost of prediction accuracy.

In reinforcement learning, an agent attempts to learn high-performing behaviors through interacting with the environment, such behaviors are often quantified in the form of a reward function. However some aspects of behavior, such as ones which are deemed unsafe and are to be avoided, are best captured through constraints. We propose a novel approach called First Order Constrained Optimization in Policy Space (FOCOPS) which maximizes an agent's overall reward while ensuring the agent satisfies a set of cost constraints. Using data generated from the current policy, FOCOPS first finds the optimal update policy by solving a constrained optimization problem in the nonparameterized policy space. FOCOPS then projects the update policy back into the parametric policy space. Our approach provides a guarantee for constraint satisfaction throughout training and is first-order in nature therefore extremely simple to implement. We provide empirical evidence that our algorithm achieves better performance on a set of constrained robotics locomotive tasks compared to current state of the art approaches.

We present a new algorithmic approach for the task of finding a chordal Markov network structure that maximizes a given scoring function. The algorithm is based on branch and bound and integrates dynamic programming for both domain pruning and for obtaining strong bounds for search-space pruning. Empirically, we show that the approach dominates in terms of running times a recent integer programming approach (and thereby also a recent constraint optimization approach) for the problem. Papers published at the Neural Information Processing Systems Conference.