The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when they are not. Most previous work has assumed that the algorithm has access to a single predictor. However, in practice, there are many machine learning methods available, often with incomparable generalization guarantees, making it hard to pick a best method a priori. In this work we consider scenarios where multiple predictors are available to the algorithm and the question is how to best utilize them. Ideally, we would like the algorithm's performance to depend on the quality of the best predictor. However, utilizing more predictions comes with a cost, since we now have to identify which prediction is the best. We study the use of multiple predictors for a number of fundamental problems, including matching, load balancing, and non-clairvoyant scheduling, which have been well-studied in the single predictor setting. For each of these problems we introduce new algorithms that take advantage of multiple predictors, and prove bounds on the resulting performance.
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Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating the marginals of the probability distribution which is uniform over satisfying configurations). This paper presents new algorithms for the latter framework, ultimately producing estimates for satisfying configurations using methods from Boolean Fourier analysis. The approach is broadly inspired by the quantum amplitude amplification algorithm in that it maximally increases the amplitude of the approximation function over satisfying configurations given sequential refinements. We demonstrate that satisfying solutions may be retrieved in a process analogous to quantum measurement made efficient by sparsity in the Fourier domain, and present a complete solver construction using this novel approximation. Freedom in the refinement strategy invites further opportunities to design solvers in an evolutionary computing framework. Results demonstrate competitive performance against local solvers for the Boolean satisfiability (SAT) problem, encouraging future work in understanding the connections between Boolean Fourier analysis and constraint satisfaction.
As ride-hailing services become increasingly popular, being able to accurately predict demand for such services can help operators efficiently allocate drivers to customers, and reduce idle time, improve congestion, and enhance the passenger experience. This paper proposes UberNet, a deep learning Convolutional Neural Network for short-term prediction of demand for ride-hailing services. UberNet empploys a multivariate framework that utilises a number of temporal and spatial features that have been found in the literature to explain demand for ride-hailing services. The proposed model includes two sub-networks that aim to encode the source series of various features and decode the predicting series, respectively. To assess the performance and effectiveness of UberNet, we use 9 months of Uber pickup data in 2014 and 28 spatial and temporal features from New York City. By comparing the performance of UberNet with several other approaches, we show that the prediction quality of the model is highly competitive. Further, Ubernet's prediction performance is better when using economic, social and built environment features. This suggests that Ubernet is more naturally suited to including complex motivators in making real-time passenger demand predictions for ride-hailing services.
This work studies the problem of transfer learning under the functional linear regression model framework, which aims to improve the estimation and prediction of the target model by leveraging the information from related source models. We measure the relatedness between target and source models using Reproducing Kernel Hilbert Spaces (RKHS) norm, allowing the type of information being transferred to be interpreted by the structural properties of the spaces. Two transfer learning algorithms are proposed: one transfers information from source tasks when we know which sources to use, while the other one aggregates multiple transfer learning results from the first algorithm to achieve robust transfer learning without prior information about the sources. Furthermore, we establish the optimal convergence rates for the prediction risk in the target model, making the statistical gain via transfer learning mathematically provable. The theoretical analysis of the prediction risk also provides insights regarding what factors are affecting the transfer learning effect, i.e. what makes source tasks useful to the target task. We demonstrate the effectiveness of the proposed transfer learning algorithms on extensive synthetic data as well as real financial data application.
Retrieval-augmented Neural Machine Translation models have been successful in many translation scenarios. Different from previous works that make use of mutually similar but redundant translation memories~(TMs), we propose a new retrieval-augmented NMT to model contrastively retrieved translation memories that are holistically similar to the source sentence while individually contrastive to each other providing maximal information gains in three phases. First, in TM retrieval phase, we adopt a contrastive retrieval algorithm to avoid redundancy and uninformativeness of similar translation pieces. Second, in memory encoding stage, given a set of TMs we propose a novel Hierarchical Group Attention module to gather both local context of each TM and global context of the whole TM set. Finally, in training phase, a Multi-TM contrastive learning objective is introduced to learn salient feature of each TM with respect to target sentence. Experimental results show that our framework obtains improvements over strong baselines on the benchmark datasets.
Exploratory factor analysis (EFA) has been widely used to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that are widely used to find interpretable loading matrices. This paper proposes a new family of oblique rotations based on component-wise $L^p$ loss functions $(0 < p\leq 1)$ that is closely related to an $L^p$ regularised estimator. Model selection and post-selection inference procedures are developed based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are non-smooth, an iteratively reweighted gradient projection algorithm is developed to solve the optimisation problem. Theoretical results are developed that establish the statistical consistency of the estimation, model selection, and post-selection inference. The proposed method is evaluated and compared with regularised estimation and traditional rotation methods via simulation studies. It is further illustrated by an application to the big-five personality assessment.
Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the cost of computational efficiency is a reduction in performance; fewer samples results in noisier updates. We show that we can contend with this noise by learning how to update the control distribution more effectively and make better use of the few samples that we have. Our learned controllers are trained via imitation learning to mimic an expert which has access to substantially more samples. We test the efficacy of our approach on multiple simulated robotics tasks in sample-constrained regimes and demonstrate that our approach can outperform a MPC controller with the same number of samples.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.
Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.
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