Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Although provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open research problem, often tackled by assuming an additive structure for $f$. However, such algorithms introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. In this paper, we relax the restrictive assumptions on the additive structure of $f$, at the expense of weakening the maximization guarantees of the acquisition function, and we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ does not exist or comprises high-dimensional factors.
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A key challenge in Bayesian decentralized data fusion is the `rumor propagation' or `double counting' phenomenon, where previously sent data circulates back to its sender. It is often addressed by approximate methods like covariance intersection (CI) which takes a weighted average of the estimates to compute the bound. The problem is that this bound is not tight, i.e. the estimate is often over-conservative. In this paper, we show that by exploiting the probabilistic independence structure in multi-agent decentralized fusion problems a tighter bound can be found using (i) an expansion to the CI algorithm that uses multiple (non-monolithic) weighting factors instead of one (monolithic) factor in the original CI and (ii) a general optimization scheme that is able to compute optimal bounds and fully exploit an arbitrary dependency structure. We compare our methods and show that on a simple problem, they converge to the same solution. We then test our new non-monolithic CI algorithm on a large-scale target tracking simulation and show that it achieves a tighter bound and a more accurate estimate compared to the original monolithic CI.
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.
Graph learning has a wide range of applications in many scenarios, which require more need for data privacy. Federated learning is an emerging distributed machine learning approach that leverages data from individual devices or data centers to improve the accuracy and generalization of the model, while also protecting the privacy of user data. Graph-federated learning is mainly based on the classical federated learning framework i.e., the Client-Server framework. However, the Client-Server framework faces problems such as a single point of failure of the central server and poor scalability of network topology. First, we introduce the decentralized framework to graph-federated learning. Second, determine the confidence among nodes based on the similarity of data among nodes, subsequently, the gradient information is then aggregated by linear weighting based on confidence. Finally, the proposed method is compared with FedAvg, Fedprox, GCFL, and GCFL+ to verify the effectiveness of the proposed method. Experiments demonstrate that the proposed method outperforms other methods.
Obtaining accurate probabilistic forecasts while respecting hierarchical information is an important operational challenge in many applications, perhaps most obviously in energy management, supply chain planning, and resource allocation. The basic challenge, especially for multivariate forecasting, is that forecasts are often required to be coherent with respect to the hierarchical structure. In this paper, we propose a new model which leverages a factor model structure to produce coherent forecasts by construction. This is a consequence of a simple (exchangeability) observation: permuting \textit{}base-level series in the hierarchy does not change their aggregates. Our model uses a convolutional neural network to produce parameters for the factors, their loadings and base-level distributions; it produces samples which can be differentiated with respect to the model's parameters; and it can therefore optimize for any sample-based loss function, including the Continuous Ranked Probability Score and quantile losses. We can choose arbitrary continuous distributions for the factor and the base-level distributions. We compare our method to two previous methods which can be optimized end-to-end, while enforcing coherent aggregation. Our model achieves significant improvements: between $11.8-41.4\%$ on three hierarchical forecasting datasets. We also analyze the influence of parameters in our model with respect to base-level distribution and number of factors.
Maximizing long-term rewards is the primary goal in sequential decision-making problems. The majority of existing methods assume that side information is freely available, enabling the learning agent to observe all features' states before making a decision. In real-world problems, however, collecting beneficial information is often costly. That implies that, besides individual arms' reward, learning the observations of the features' states is essential to improve the decision-making strategy. The problem is aggravated in a non-stationary environment where reward and cost distributions undergo abrupt changes over time. To address the aforementioned dual learning problem, we extend the contextual bandit setting and allow the agent to observe subsets of features' states. The objective is to maximize the long-term average gain, which is the difference between the accumulated rewards and the paid costs on average. Therefore, the agent faces a trade-off between minimizing the cost of information acquisition and possibly improving the decision-making process using the obtained information. To this end, we develop an algorithm that guarantees a sublinear regret in time. Numerical results demonstrate the superiority of our proposed policy in a real-world scenario.
For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed efficiently. With this in mind, we take a distributional approach and introduce a novel dominance criterion relating return distributions of policies directly. Based on this criterion, we present the distributional undominated set and show that it contains optimal policies otherwise ignored by the Pareto front. In addition, we propose the convex distributional undominated set and prove that it comprises all policies that maximise expected utility for multivariate risk-averse decision makers. We propose a novel algorithm to learn the distributional undominated set and further contribute pruning operators to reduce the set to the convex distributional undominated set. Through experiments, we demonstrate the feasibility and effectiveness of these methods, making this a valuable new approach for decision support in real-world problems.
In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise sparsity and element-wise sparsity in each group. By combining the Gilbert-Varshamov bound and its variants, we develop a novel lower bound technique for the metric entropy of the parameter space, specifically tailored for the double sparse structure over $\ell_u(\ell_q)$-balls with $u,q \in [0,1]$. We prove lower bounds on the estimation error using an information-theoretic approach, leveraging our proposed lower bound technique and Fano's inequality. To complement the lower bounds, we establish matching upper bounds through a direct analysis of constrained least-squares estimators and utilize results from empirical processes. A significant finding of our study is the discovery of a phase transition phenomenon in the minimax rates for $u,q \in (0, 1]$. Furthermore, we extend the theoretical results to the double sparse regression model and determine its minimax rate for estimation error. To tackle double sparse linear regression, we develop the DSIHT (Double Sparse Iterative Hard Thresholding) algorithm, demonstrating its optimality in the minimax sense. Finally, we demonstrate the superiority of our method through numerical experiments.
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature: parameter characterizing subgroup classification is not identified under the null hypothesis of no subgroup. Due to this irregularity, the existing methods have the following two limitations. First, the asymptotic null distribution of test statistics often takes an intractable form, which necessitates computationally demanding resampling methods to calculate the critical value. Second, the dimension of personal attributes characterizing subgroup membership is not allowed to be of high dimension. To solve these two problems simultaneously, this study develops a novel shrinkage likelihood ratio test for the existence of a subgroup using a logistic-normal mixture model. The proposed test statistics are built on a modified likelihood function that shrinks possibly high-dimensional unidentified parameters toward zero under the null hypothesis while retaining power under the alternative. This shrinkage helps handle the irregularity and restore the simple chi-square-type asymptotics even under the high-dimensional regime.
Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of constraint, while many real-world problems often involve several constraints. In this paper, we consider the problem of submodular maximization under the intersection of two commonly used constraints, i.e., $k$-matroid constraint and $m$-knapsack constraint, and propose a new algorithm SPROUT by incorporating partial enumeration into the simultaneous greedy framework. We prove that SPROUT can achieve a polynomial-time approximation guarantee better than the state-of-the-art algorithms. Then, we introduce the random enumeration and smooth techniques into SPROUT to improve its efficiency, resulting in the SPROUT++ algorithm, which can keep a similar approximation guarantee. Experiments on the applications of movie recommendation and weighted max-cut demonstrate the superiority of SPROUT++ in practice.
In recent years, mobile devices have gained increasingly development with stronger computation capability and larger storage. Some of the computation-intensive machine learning and deep learning tasks can now be run on mobile devices. To take advantage of the resources available on mobile devices and preserve users' privacy, the idea of mobile distributed machine learning is proposed. It uses local hardware resources and local data to solve machine learning sub-problems on mobile devices, and only uploads computation results instead of original data to contribute to the optimization of the global model. This architecture can not only relieve computation and storage burden on servers, but also protect the users' sensitive information. Another benefit is the bandwidth reduction, as various kinds of local data can now participate in the training process without being uploaded to the server. In this paper, we provide a comprehensive survey on recent studies of mobile distributed machine learning. We survey a number of widely-used mobile distributed machine learning methods. We also present an in-depth discussion on the challenges and future directions in this area. We believe that this survey can demonstrate a clear overview of mobile distributed machine learning and provide guidelines on applying mobile distributed machine learning to real applications.
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