Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability distribution. The performance of IS heavily depends on the appropriate selection of the proposal distributions where the samples are simulated from. In this paper, we propose an adaptive importance sampler, called GRAMIS, that iteratively improves the set of proposals. The algorithm exploits geometric information of the target to adapt the location and scale parameters of those proposals. Moreover, in order to allow for a cooperative adaptation, a repulsion term is introduced that favors a coordinated exploration of the state space. This translates into a more diverse exploration and a better approximation of the target via the mixture of proposals. Moreover, we provide a theoretical justification of the repulsion term. We show the good performance of GRAMIS in two problems where the target has a challenging shape and cannot be easily approximated by a standard uni-modal proposal.
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Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, the federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples $O(\epsilon^{-3})$ and $O(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms.
This paper proposes Distributed Model Predictive Covariance Steering (DMPCS), a novel method for safe multi-robot control under uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single methodology that is safe, scalable and decentralized. Initially, we pose a problem formulation that uses the Wasserstein distance to steer the state distributions of a multi-robot team to desired targets, and probabilistic constraints to ensure safety. We then transform this problem into a finite-dimensional optimization one by utilizing a disturbance feedback policy parametrization for covariance steering and a tractable approximation of the safety constraints. To solve the latter problem, we derive a decentralized consensus-based algorithm using the Alternating Direction Method of Multipliers (ADMM). This method is then extended to a receding horizon form, which yields the proposed DMPCS algorithm. Simulation experiments on large-scale problems with up to hundreds of robots successfully demonstrate the effectiveness and scalability of DMPCS. Its superior capability in achieving safety is also highlighted through a comparison against a standard stochastic MPC approach. A video with all simulation experiments is available in //youtu.be/Hks-0BRozxA.
Privacy in AI remains a topic that draws attention from researchers and the general public in recent years. As one way to implement privacy-preserving AI, differentially private learning is a framework that enables AI models to use differential privacy (DP). To achieve DP in the learning process, existing algorithms typically limit the magnitude of gradients with a constant clipping, which requires carefully tuned due to its significant impact on model performance. As a solution to this issue, latest works NSGD and Auto-S innovatively propose to use normalization instead of clipping to avoid hyperparameter tuning. However, normalization-based approaches like NSGD and Auto-S rely on a monotonic weight function, which imposes excessive weight on small gradient samples and introduces extra deviation to the update. In this paper, we propose a Differentially Private Per-Sample Adaptive Clipping (DP-PSAC) algorithm based on a non-monotonic adaptive weight function, which guarantees privacy without the typical hyperparameter tuning process of using a constant clipping while significantly reducing the deviation between the update and true batch-averaged gradient. We provide a rigorous theoretical convergence analysis and show that with convergence rate at the same order, the proposed algorithm achieves a lower non-vanishing bound, which is maintained over training iterations, compared with NSGD/Auto-S. In addition, through extensive experimental evaluation, we show that DP-PSAC outperforms or matches the state-of-the-art methods on multiple main-stream vision and language tasks.
Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.
Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, and as such the identification of model orders remains a fundamental task. We propose a novel method of ARMA order identification through projection predictive inference, which is grounded in Bayesian decision theory and naturally allows for uncertainty communication. It benefits from improved stability through the use of a reference model. The procedure consists of two steps: in the first, the practitioner incorporates their understanding of underlying data-generating process into a reference model, which we latterly project onto possibly parsimonious submodels. These submodels are optimally inferred to best replicate the predictive performance of the reference model. We further propose a search heuristic amenable to the ARMA framework. We show that the submodels selected by our procedure exhibit predictive performance at least as good as those produced by auto.arima over simulated and real-data experiments, and in some cases out-perform the latter. Finally we show that our procedure is robust to noise, and scales well to larger data.
In recent years, multi-scale generative adversarial networks (GANs) have been proposed to build generalized image processing models based on single sample. Constraining on the sample size, multi-scale GANs have much difficulty converging to the global optimum, which ultimately leads to limitations in their capabilities. In this paper, we pioneered the introduction of PAC-Bayes generalized bound theory into the training analysis of specific models under different adversarial training methods, which can obtain a non-vacuous upper bound on the generalization error for the specified multi-scale GAN structure. Based on the drastic changes we found of the generalization error bound under different adversarial attacks and different training states, we proposed an adaptive training method which can greatly improve the image manipulation ability of multi-scale GANs. The final experimental results show that our adaptive training method in this paper has greatly contributed to the improvement of the quality of the images generated by multi-scale GANs on several image manipulation tasks. In particular, for the image super-resolution restoration task, the multi-scale GAN model trained by the proposed method achieves a 100% reduction in natural image quality evaluator (NIQE) and a 60% reduction in root mean squared error (RMSE), which is better than many models trained on large-scale datasets.
Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval with $n$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search methods with $O(\log n)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategy, we investigate in detail the $p$-dimensional Gaussian changing means setup, including high-dimensional scenarios. For some of our proposals, we prove asymptotic minimax optimality for detecting change points and derive their asymptotic localization rate. These rates (up to a possible log factor) are optimal for the univariate and multivariate scenarios, and are by far the fastest in the literature under the weakest possible detection condition on the signal-to-noise ratio in the high-dimensional scenario. Computationally, our proposed methodology has the worst case complexity of $O(np)$, which can be improved to be sublinear in $n$ if some a-priori knowledge on the length of the shortest segment is available. Our search strategies generalize far beyond the theoretically analyzed setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models.
In this paper we address the solution of the popular Wordle puzzle, using new reinforcement learning methods, which apply more generally to adaptive control of dynamic systems and to classes of Partially Observable Markov Decision Process (POMDP) problems. These methods are based on approximation in value space and the rollout approach, admit a straightforward implementation, and provide improved performance over various heuristic approaches. For the Wordle puzzle, they yield on-line solution strategies that are very close to optimal at relatively modest computational cost. Our methods are viable for more complex versions of Wordle and related search problems, for which an optimal strategy would be impossible to compute. They are also applicable to a wide range of adaptive sequential decision problems that involve an unknown or frequently changing environment whose parameters are estimated on-line.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.
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