Risk-averse learning with delayed feedback

In real-world scenarios, the impacts of decisions may not manifest immediately. Taking these delays into account facilitates accurate assessment and management of risk in real-world environments, thereby ensuring the efficacy of strategies. In this paper, we investigate risk-averse learning using Conditional Value at Risk (CVaR) as risk measure, while incorporating delayed feedback with unknown but bounded delays. We develop two risk-averse learning algorithms that rely on one-point and two-point zeroth-order optimization approaches, respectively. The regret achieved by the algorithms is analyzed in terms of the cumulative delay and the number of total samplings. The results suggest that the two-point risk-averse learning achieves a smaller regret bound than the one-point algorithm. Furthermore, the one-point risk-averse learning algorithm attains sublinear regret under certain delay conditions, and the two-point risk-averse learning algorithm achieves sublinear regret with minimal restrictions on the delay. We provide numerical experiments on a dynamic pricing problem to demonstrate the performance of the proposed algorithms.

Federated Cubic Regularized Newton Learning with Sparsification-amplified Differential Privacy

This paper investigates the use of the cubic-regularized Newton method within a federated learning framework while addressing two major concerns that commonly arise in federated learning: privacy leakage and communication bottleneck. We introduce a federated learning algorithm called Differentially Private Federated Cubic Regularized Newton (DP-FCRN). By leveraging second-order techniques, our algorithm achieves lower iteration complexity compared to first-order methods. We also incorporate noise perturbation during local computations to ensure privacy. Furthermore, we employ sparsification in uplink transmission, which not only reduces the communication costs but also amplifies the privacy guarantee. Specifically, this approach reduces the necessary noise intensity without compromising privacy protection. We analyze the convergence properties of our algorithm and establish the privacy guarantee. Finally, we validate the effectiveness of the proposed algorithm through experiments on a benchmark dataset.

Real-time Hybrid System Identification with Online Deterministic Annealing

We introduce a real-time identification method for discrete-time state-dependent switching systems in both the input--output and state-space domains. In particular, we design a system of adaptive algorithms running in two timescales; a stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale and estimates the mode-switching signal, and an recursive identification algorithm runs at a faster timescale and updates the parameters of the local models based on the estimate of the switching signal. We first focus on piece-wise affine systems and discuss identifiability conditions and convergence properties based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for switched systems, the proposed approach gradually estimates the number of modes and is appropriate for real-time system identification using sequential data acquisition. The progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off. Finally, we address specific challenges that arise in the application of the proposed methodology in identification of more general switching systems. Simulation results validate the efficacy of the proposed methodology.

Exploring the Effectiveness of Object-Centric Representations in Visual Question Answering: Comparative Insights with Foundation Models

Object-centric (OC) representations, which represent the state of a visual scene by modeling it as a composition of objects, have the potential to be used in various downstream tasks to achieve systematic compositional generalization and facilitate reasoning. However, these claims have not been thoroughly analyzed yet. Recently, foundation models have demonstrated unparalleled capabilities across diverse domains from language to computer vision, marking them as a potential cornerstone of future research for a multitude of computational tasks. In this paper, we conduct an extensive empirical study on representation learning for downstream Visual Question Answering (VQA), which requires an accurate compositional understanding of the scene. We thoroughly investigate the benefits and trade-offs of OC models and alternative approaches including large pre-trained foundation models on both synthetic and real-world data, and demonstrate a viable way to achieve the best of both worlds. The extensiveness of our study, encompassing over 800 downstream VQA models and 15 different types of upstream representations, also provides several additional insights that we believe will be of interest to the community at large.

Challenges and Considerations in the Evaluation of Bayesian Causal Discovery

Representing uncertainty in causal discovery is a crucial component for experimental design, and more broadly, for safe and reliable causal decision making. Bayesian Causal Discovery (BCD) offers a principled approach to encapsulating this uncertainty. Unlike non-Bayesian causal discovery, which relies on a single estimated causal graph and model parameters for assessment, evaluating BCD presents challenges due to the nature of its inferred quantity - the posterior distribution. As a result, the research community has proposed various metrics to assess the quality of the approximate posterior. However, there is, to date, no consensus on the most suitable metric(s) for evaluation. In this work, we reexamine this question by dissecting various metrics and understanding their limitations. Through extensive empirical evaluation, we find that many existing metrics fail to exhibit a strong correlation with the quality of approximation to the true posterior, especially in scenarios with low sample sizes where BCD is most desirable. We highlight the suitability (or lack thereof) of these metrics under two distinct factors: the identifiability of the underlying causal model and the quantity of available data. Both factors affect the entropy of the true posterior, indicating that the current metrics are less fitting in settings of higher entropy. Our findings underline the importance of a more nuanced evaluation of new methods by taking into account the nature of the true posterior, as well as guide and motivate the development of new evaluation procedures for this challenge.

Diffusion Based Causal Representation Learning

Causal reasoning can be considered a cornerstone of intelligent systems. Having access to an underlying causal graph comes with the promise of cause-effect estimation and the identification of efficient and safe interventions. However, learning causal representations remains a major challenge, due to the complexity of many real-world systems. Previous works on causal representation learning have mostly focused on Variational Auto-Encoders (VAE). These methods only provide representations from a point estimate, and they are unsuitable to handle high dimensions. To overcome these problems, we proposed a new Diffusion-based Causal Representation Learning (DCRL) algorithm. This algorithm uses diffusion-based representations for causal discovery. DCRL offers access to infinite dimensional latent codes, which encode different levels of information in the latent code. In a first proof of principle, we investigate the use of DCRL for causal representation learning. We further demonstrate experimentally that this approach performs comparably well in identifying the causal structure and causal variables.

Sensor Fault Detection and Isolation in Autonomous Nonlinear Systems Using Neural Network-Based Observers

This paper presents a new observer-based approach to detect and isolate faulty sensors in industrial systems. Two types of sensor faults are considered: complete failure and sensor deterioration. The proposed method is applicable to general autonomous nonlinear systems without making any assumptions about its triangular and/or normal form, which is usually considered in the observer design literature. The key aspect of our approach is a learning-based design of the Luenberger observer, which involves using a neural network to approximate the injective map that transforms the nonlinear system into a stable linear system with output injection. This learning-based Luenberger observer accurately estimates the system's state, allowing for the detection of sensor faults through residual generation. The residual is computed as the norm of the difference between the system's measured output and the observer's predicted output vectors. Fault isolation is achieved by comparing each sensor's measurement with its corresponding predicted value. We demonstrate the effectiveness of our approach in capturing and isolating sensor faults while remaining robust in the presence of measurement noise and system uncertainty. We validate our method through numerical simulations of sensor faults in a network of Kuramoto oscillators.

Estimating a scalar log-concave random variable, using a silence set based probabilistic sampling

We study the probabilistic sampling of a random variable, in which the variable is sampled only if it falls outside a given set, which is called the silence set. This helps us to understand optimal event-based sampling for the special case of IID random processes, and also to understand the design of a sub-optimal scheme for other cases. We consider the design of this probabilistic sampling for a scalar, log-concave random variable, to minimize either the mean square estimation error, or the mean absolute estimation error. We show that the optimal silence interval: (i) is essentially unique, and (ii) is the limit of an iterative procedure of centering. Further we show through numerical experiments that super-level intervals seem to be remarkably near-optimal for mean square estimation. Finally we use the Gauss inequality for scalar unimodal densities, to show that probabilistic sampling gives a mean square distortion that is less than a third of the distortion incurred by periodic sampling, if the average sampling rate is between 0.3 and 0.9 samples per tick.

Shared Situational Awareness with V2X Communication and Set-membership Estimation

The ability to perceive and comprehend a traffic situation and to predict the intent of vehicles and road-users in the surrounding of the ego-vehicle is known as situational awareness. Situational awareness for a heavy-duty autonomous vehicle is a critical part of the automation platform and is dependent on the ego-vehicle's field-of-view. But when it comes to the urban scenario, the field-of-view of the ego-vehicle is likely to be affected by occlusion and blind spots caused by infrastructure, moving vehicles, and parked vehicles. This paper proposes a framework to improve situational awareness using set-membership estimation and vehicle-to-everything (V2X) communication. This framework provides safety guarantees and can adapt to dynamically changing scenarios, and is integrated into an existing complex autonomous platform. A detailed description of the framework implementation and real-time results are illustrated in this paper.

Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

The design of Luenberger observers for nonlinear systems involves state transformation to another coordinate system where the dynamics are asymptotically stable and linear up to output injection. The observer then provides a state estimate in the original coordinates by inverting the transformation map. For general nonlinear systems, however, the main challenge is to find such a transformation and to ensure that it is injective. This paper addresses this challenge by proposing a learning method that employs supervised physics-informed neural networks to approximate both the transformation and its inverse. It is shown that the proposed method exhibits better generalization capabilities than other contemporary methods. Moreover, the observer is shown to be robust under the neural network's approximation error and the system uncertainties.