We consider the problem of optimising an expensive-to-evaluate grey-box objective function, within a finite budget, where known side-information exists in the form of the causal structure between the design variables. Standard black-box optimisation ignores the causal structure, often making it inefficient and expensive. The few existing methods that consider the causal structure are myopic and do not fully accommodate the observation-intervention trade-off that emerges when estimating causal effects. In this paper, we show that the observation-intervention trade-off can be formulated as a non-myopic optimal stopping problem which permits an efficient solution. We give theoretical results detailing the structure of the optimal stopping times and demonstrate the generality of our approach by showing that it can be integrated with existing causal Bayesian optimisation algorithms. Experimental results show that our formulation can enhance existing algorithms on real and synthetic benchmarks.
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Existing methods have demonstrated effective performance on a single degradation type. In practical applications, however, the degradation is often unknown, and the mismatch between the model and the degradation will result in a severe performance drop. In this paper, we propose an all-in-one image restoration network that tackles multiple degradations. Due to the heterogeneous nature of different types of degradations, it is difficult to process multiple degradations in a single network. To this end, we propose to learn a neural degradation representation (NDR) that captures the underlying characteristics of various degradations. The learned NDR decomposes different types of degradations adaptively, similar to a neural dictionary that represents basic degradation components. Subsequently, we develop a degradation query module and a degradation injection module to effectively recognize and utilize the specific degradation based on NDR, enabling the all-in-one restoration ability for multiple degradations. Moreover, we propose a bidirectional optimization strategy to effectively drive NDR to learn the degradation representation by optimizing the degradation and restoration processes alternately. Comprehensive experiments on representative types of degradations (including noise, haze, rain, and downsampling) demonstrate the effectiveness and generalization capability of our method.
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.
Generative retrieval, which is a new advanced paradigm for document retrieval, has recently attracted research interests, since it encodes all documents into the model and directly generates the retrieved documents. However, its power is still underutilized since it heavily relies on the "preprocessed" document identifiers (docids), thus limiting its retrieval performance and ability to retrieve new documents. In this paper, we propose a novel fully end-to-end retrieval paradigm. It can not only end-to-end learn the best docids for existing and new documents automatically via a semantic indexing module, but also perform end-to-end document retrieval via an encoder-decoder-based generative model, namely Auto Search Indexer (ASI). Besides, we design a reparameterization mechanism to combine the above two modules into a joint optimization framework. Extensive experimental results demonstrate the superiority of our model over advanced baselines on both public and industrial datasets and also verify the ability to deal with new documents.
Consider the following problem: given a few demonstrations of a task across a few different objects, how can a robot learn to perform that same task on new, previously unseen objects? This is challenging because the large variety of objects within a class makes it difficult to infer the task-relevant relationship between the new objects and the objects in the demonstrations. We address this by formulating imitation learning as a conditional alignment problem between graph representations of objects. Consequently, we show that this conditioning allows for in-context learning, where a robot can perform a task on a set of new objects immediately after the demonstrations, without any prior knowledge about the object class or any further training. In our experiments, we explore and validate our design choices, and we show that our method is highly effective for few-shot learning of several real-world, everyday tasks, whilst outperforming baselines. Videos are available on our project webpage at //www.robot-learning.uk/implicit-graph-alignment.
We consider the problem of active learning in the context of spatial sampling for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible. We present a finite-horizon search procedure to perform LSE in one dimension while optimally balancing both the final estimation error and the distance traveled for a fixed number of samples. A tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem. We then show how this approach can be used to perform level set estimation in higher dimensions under the popular Gaussian process model. Empirical results on synthetic data indicate that as the cost of travel increases, our method's ability to treat distance nonmyopically allows it to significantly improve on the state of the art. On real air quality data, our approach achieves roughly one fifth the estimation error at less than half the cost of competing algorithms.
Gaussian mixtures are widely used for approximating density functions in various applications such as density estimation, belief propagation, and Bayesian filtering. These applications often utilize Gaussian mixtures as initial approximations that are updated recursively. A key challenge in these recursive processes stems from the exponential increase in the mixture's order, resulting in intractable inference. To overcome the difficulty, the Gaussian mixture reduction (GMR), which approximates a high order Gaussian mixture by one with a lower order, can be used. Although existing clustering-based methods are known for their satisfactory performance and computational efficiency, their convergence properties and optimal targets remain unknown. In this paper, we propose a novel optimization-based GMR method based on composite transportation divergence (CTD). We develop a majorization-minimization algorithm for computing the reduced mixture and establish its theoretical convergence under general conditions. Furthermore, we demonstrate that many existing clustering-based methods are special cases of ours, effectively bridging the gap between optimization-based and clustering-based techniques. Our unified framework empowers users to select the most appropriate cost function in CTD to achieve superior performance in their specific applications. Through extensive empirical experiments, we demonstrate the efficiency and effectiveness of our proposed method, showcasing its potential in various domains.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
We examine the problem of question answering over knowledge graphs, focusing on simple questions that can be answered by the lookup of a single fact. Adopting a straightforward decomposition of the problem into entity detection, entity linking, relation prediction, and evidence combination, we explore simple yet strong baselines. On the popular SimpleQuestions dataset, we find that basic LSTMs and GRUs plus a few heuristics yield accuracies that approach the state of the art, and techniques that do not use neural networks also perform reasonably well. These results show that gains from sophisticated deep learning techniques proposed in the literature are quite modest and that some previous models exhibit unnecessary complexity.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
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