We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.
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We consider the problem of predictive monitoring (PM), i.e., predicting at runtime the satisfaction of a desired property from the current system's state. Due to its relevance for runtime safety assurance and online control, PM methods need to be efficient to enable timely interventions against predicted violations, while providing correctness guarantees. We introduce \textit{quantitative predictive monitoring (QPM)}, the first PM method to support stochastic processes and rich specifications given in Signal Temporal Logic (STL). Unlike most of the existing PM techniques that predict whether or not some property $\phi$ is satisfied, QPM provides a quantitative measure of satisfaction by predicting the quantitative (aka robust) STL semantics of $\phi$. QPM derives prediction intervals that are highly efficient to compute and with probabilistic guarantees, in that the intervals cover with arbitrary probability the STL robustness values relative to the stochastic evolution of the system. To do so, we take a machine-learning approach and leverage recent advances in conformal inference for quantile regression, thereby avoiding expensive Monte-Carlo simulations at runtime to estimate the intervals. We also show how our monitors can be combined in a compositional manner to handle composite formulas, without retraining the predictors nor sacrificing the guarantees. We demonstrate the effectiveness and scalability of QPM over a benchmark of four discrete-time stochastic processes with varying degrees of complexity.
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.
Reinforcement Learning aims at identifying and evaluating efficient control policies from data. In many real-world applications, the learner is not allowed to experiment and cannot gather data in an online manner (this is the case when experimenting is expensive, risky or unethical). For such applications, the reward of a given policy (the target policy) must be estimated using historical data gathered under a different policy (the behavior policy). Most methods for this learning task, referred to as Off-Policy Evaluation (OPE), do not come with accuracy and certainty guarantees. We present a novel OPE method based on Conformal Prediction that outputs an interval containing the true reward of the target policy with a prescribed level of certainty. The main challenge in OPE stems from the distribution shift due to the discrepancies between the target and the behavior policies. We propose and empirically evaluate different ways to deal with this shift. Some of these methods yield conformalized intervals with reduced length compared to existing approaches, while maintaining the same certainty level.
We develop a new framework for embedding joint probability distributions in tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon-Nikodym derivative, which we estimate from sample sizes of up to several million data points, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. The embedding is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.
Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over $T$ time steps with confidence $1-\delta$, {previous works require that each individual prediction region is valid} with confidence $1-\delta/T$. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on a case study using pedestrian trajectory predictors.
The dynamic scheduling of ultra-reliable and low-latency traffic (URLLC) in the uplink can significantly enhance the efficiency of coexisting services, such as enhanced mobile broadband (eMBB) devices, by only allocating resources when necessary. The main challenge is posed by the uncertainty in the process of URLLC packet generation, which mandates the use of predictors for URLLC traffic in the coming frames. In practice, such prediction may overestimate or underestimate the amount of URLLC data to be generated, yielding either an excessive or an insufficient amount of resources to be pre-emptively allocated for URLLC packets. In this paper, we introduce a novel scheduler for URLLC packets that provides formal guarantees on reliability and latency irrespective of the quality of the URLLC traffic predictor. The proposed method leverages recent advances in online conformal prediction (CP), and follows the principle of dynamically adjusting the amount of allocated resources so as to meet reliability and latency requirements set by the designer.
Federated Learning (FL) has recently emerged as a popular framework, which allows resource-constrained discrete clients to cooperatively learn the global model under the orchestration of a central server while storing privacy-sensitive data locally. However, due to the difference in equipment and data divergence of heterogeneous clients, there will be parameter deviation between local models, resulting in a slow convergence rate and a reduction of the accuracy of the global model. The current FL algorithms use the static client learning strategy pervasively and can not adapt to the dynamic training parameters of different clients. In this paper, by considering the deviation between different local model parameters, we propose an adaptive learning rate scheme for each client based on entropy theory to alleviate the deviation between heterogeneous clients and achieve fast convergence of the global model. It's difficult to design the optimal dynamic learning rate for each client as the local information of other clients is unknown, especially during the local training epochs without communications between local clients and the central server. To enable a decentralized learning rate design for each client, we first introduce mean-field schemes to estimate the terms related to other clients' local model parameters. Then the decentralized adaptive learning rate for each client is obtained in closed form by constructing the Hamilton equation. Moreover, we prove that there exist fixed point solutions for the mean-field estimators, and an algorithm is proposed to obtain them. Finally, extensive experimental results on real datasets show that our algorithm can effectively eliminate the deviation between local model parameters compared to other recent FL algorithms.
We consider perception-based control using state estimates that are obtained from high-dimensional sensor measurements via learning-enabled perception maps. However, these perception maps are not perfect and result in state estimation errors that can lead to unsafe system behavior. Stochastic sensor noise can make matters worse and result in estimation errors that follow unknown distributions. We propose a perception-based control framework that i) quantifies estimation uncertainty of perception maps, and ii) integrates these uncertainty representations into the control design. To do so, we use conformal prediction to compute valid state estimation regions, which are sets that contain the unknown state with high probability. We then devise a sampled-data controller for continuous-time systems based on the notion of measurement robust control barrier functions. Our controller uses idea from self-triggered control and enables us to avoid using stochastic calculus. Our framework is agnostic to the choice of the perception map, independent of the noise distribution, and to the best of our knowledge the first to provide probabilistic safety guarantees in such a setting. We demonstrate the effectiveness of our proposed perception-based controller for a LiDAR-enabled F1/10th car.
While recent studies on semi-supervised learning have shown remarkable progress in leveraging both labeled and unlabeled data, most of them presume a basic setting of the model is randomly initialized. In this work, we consider semi-supervised learning and transfer learning jointly, leading to a more practical and competitive paradigm that can utilize both powerful pre-trained models from source domain as well as labeled/unlabeled data in the target domain. To better exploit the value of both pre-trained weights and unlabeled target examples, we introduce adaptive consistency regularization that consists of two complementary components: Adaptive Knowledge Consistency (AKC) on the examples between the source and target model, and Adaptive Representation Consistency (ARC) on the target model between labeled and unlabeled examples. Examples involved in the consistency regularization are adaptively selected according to their potential contributions to the target task. We conduct extensive experiments on several popular benchmarks including CUB-200-2011, MIT Indoor-67, MURA, by fine-tuning the ImageNet pre-trained ResNet-50 model. Results show that our proposed adaptive consistency regularization outperforms state-of-the-art semi-supervised learning techniques such as Pseudo Label, Mean Teacher, and MixMatch. Moreover, our algorithm is orthogonal to existing methods and thus able to gain additional improvements on top of MixMatch and FixMatch. Our code is available at //github.com/SHI-Labs/Semi-Supervised-Transfer-Learning.
The goal of few-shot learning is to learn a classifier that generalizes well even when trained with a limited number of training instances per class. The recently introduced meta-learning approaches tackle this problem by learning a generic classifier across a large number of multiclass classification tasks and generalizing the model to a new task. Yet, even with such meta-learning, the low-data problem in the novel classification task still remains. In this paper, we propose Transductive Propagation Network (TPN), a novel meta-learning framework for transductive inference that classifies the entire test set at once to alleviate the low-data problem. Specifically, we propose to learn to propagate labels from labeled instances to unlabeled test instances, by learning a graph construction module that exploits the manifold structure in the data. TPN jointly learns both the parameters of feature embedding and the graph construction in an end-to-end manner. We validate TPN on multiple benchmark datasets, on which it largely outperforms existing few-shot learning approaches and achieves the state-of-the-art results.
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