Decision-makers often simultaneously face many related but heterogeneous learning problems. For instance, a large retailer may wish to learn product demand at different stores to solve pricing or inventory problems, making it desirable to learn jointly for stores serving similar customers; alternatively, a hospital network may wish to learn patient risk at different providers to allocate personalized interventions, making it desirable to learn jointly for hospitals serving similar patient populations. Motivated by real datasets, we study a natural setting where the unknown parameter in each learning instance can be decomposed into a shared global parameter plus a sparse instance-specific term. We propose a novel two-stage multitask learning estimator that exploits this structure in a sample-efficient way, using a unique combination of robust statistics (to learn across similar instances) and LASSO regression (to debias the results). Our estimator yields improved sample complexity bounds in the feature dimension $d$ relative to commonly-employed estimators; this improvement is exponential for "data-poor" instances, which benefit the most from multitask learning. We illustrate the utility of these results for online learning by embedding our multitask estimator within simultaneous contextual bandit algorithms. We specify a dynamic calibration of our estimator to appropriately balance the bias-variance tradeoff over time, improving the resulting regret bounds in the context dimension $d$. Finally, we illustrate the value of our approach on synthetic and real datasets.
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The Finite Element Method, an important technique in engineering, is aided by Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow for a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on task-specific heuristics or expensive error estimators, hindering their use for complex simulations. Recent learned AMR methods tackle these problems, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate the effectiveness of our approach, Adaptive Swarm Mesh Refinement (ASMR), showing that it learns reliable, scalable, and efficient refinement strategies on a set of challenging problems. Our approach significantly speeds up computation, achieving up to 30-fold improvement compared to uniform refinements in complex simulations. Additionally, we outperform learned baselines and achieve a refinement quality that is on par with a traditional error-based AMR strategy without expensive oracle information about the error signal.
In this manuscript we derive the optimal out-of-sample causal predictor for a linear system that has been observed in $k+1$ within-sample environments. In this model we consider $k$ shifted environments and one observational environment. Each environment corresponds to a linear structural equation model (SEM) with its own shift and noise vector, both in $L^2$. The strength of the shifts can be put in a certain order, and we may therefore speak of all shifts that are less or equally strong than a given shift. We consider the space of all shifts are $\gamma$ times less or equally strong than any weighted average of the observed shift vectors with weights on the unit sphere. For each $\beta\in\mathbb{R}^p$ we show that the supremum of the risk functions $R_{\tilde{A}}(\beta)$ over $\tilde{A}\in C^\gamma$ has a worst-risk decomposition into a (positive) linear combination of risk functions, depending on $\gamma$. We then define the causal regularizer, $\beta_\gamma$, as the argument $\beta$ that minimizes this risk. The main result of the paper is that this regularizer can be consistently estimated with a plug-in estimator outside a set of zero Lebesgue measure in the parameter space. A practical obstacle for such estimation is that it involves the solution of a general degree polynomial which cannot be done explicitly. Therefore we also prove that an approximate plug-in estimator using the bisection method is also consistent. An interesting by-product of the proof of the main result is that the plug-in estimation of the argmin of the maxima of a finite set of quadratic risk functions is consistent outside a set of zero Lebesgue measure in the parameter space.
Multi-fingered robotic hands have potential to enable robots to perform sophisticated manipulation tasks. However, teaching a robot to grasp objects with an anthropomorphic hand is an arduous problem due to the high dimensionality of state and action spaces. Deep Reinforcement Learning (DRL) offers techniques to design control policies for this kind of problems without explicit environment or hand modeling. However, state-of-the-art model-free algorithms have proven inefficient for learning such policies. The main problem is that the exploration of the environment is unfeasible for such high-dimensional problems, thus hampering the initial phases of policy optimization. One possibility to address this is to rely on off-line task demonstrations, but, oftentimes, this is too demanding in terms of time and computational resources. To address these problems, we propose the A Grasp Pose is All You Need (G-PAYN) method for the anthropomorphic hand of the iCub humanoid. We develop an approach to automatically collect task demonstrations to initialize the training of the policy. The proposed grasping pipeline starts from a grasp pose generated by an external algorithm, used to initiate the movement. Then a control policy (previously trained with the proposed G-PAYN) is used to reach and grab the object. We deployed the iCub into the MuJoCo simulator and use it to test our approach with objects from the YCB-Video dataset. Results show that G-PAYN outperforms current DRL techniques in the considered setting in terms of success rate and execution time with respect to the baselines. The code to reproduce the experiments is released together with the paper with an open source license.
We investigate the fixed-budget best-arm identification (BAI) problem for linear bandits in a potentially non-stationary environment. Given a finite arm set $\mathcal{X}\subset\mathbb{R}^d$, a fixed budget $T$, and an unpredictable sequence of parameters $\left\lbrace\theta_t\right\rbrace_{t=1}^{T}$, an algorithm will aim to correctly identify the best arm $x^* := \arg\max_{x\in\mathcal{X}}x^\top\sum_{t=1}^{T}\theta_t$ with probability as high as possible. Prior work has addressed the stationary setting where $\theta_t = \theta_1$ for all $t$ and demonstrated that the error probability decreases as $\exp(-T /\rho^*)$ for a problem-dependent constant $\rho^*$. But in many real-world $A/B/n$ multivariate testing scenarios that motivate our work, the environment is non-stationary and an algorithm expecting a stationary setting can easily fail. For robust identification, it is well-known that if arms are chosen randomly and non-adaptively from a G-optimal design over $\mathcal{X}$ at each time then the error probability decreases as $\exp(-T\Delta^2_{(1)}/d)$, where $\Delta_{(1)} = \min_{x \neq x^*} (x^* - x)^\top \frac{1}{T}\sum_{t=1}^T \theta_t$. As there exist environments where $\Delta_{(1)}^2/ d \ll 1/ \rho^*$, we are motivated to propose a novel algorithm $\mathsf{P1}$-$\mathsf{RAGE}$ that aims to obtain the best of both worlds: robustness to non-stationarity and fast rates of identification in benign settings. We characterize the error probability of $\mathsf{P1}$-$\mathsf{RAGE}$ and demonstrate empirically that the algorithm indeed never performs worse than G-optimal design but compares favorably to the best algorithms in the stationary setting.
Supervised classification algorithms are used to solve a growing number of real-life problems around the globe. Their performance is strictly connected with the quality of labels used in training. Unfortunately, acquiring good-quality annotations for many tasks is infeasible or too expensive to be done in practice. To tackle this challenge, active learning algorithms are commonly employed to select only the most relevant data for labeling. However, this is possible only when the quality and quantity of labels acquired from experts are sufficient. Unfortunately, in many applications, a trade-off between annotating individual samples by multiple annotators to increase label quality vs. annotating new samples to increase the total number of labeled instances is necessary. In this paper, we address the issue of faulty data annotations in the context of active learning. In particular, we propose two novel annotation unification algorithms that utilize unlabeled parts of the sample space. The proposed methods require little to no intersection between samples annotated by different experts. Our experiments on four public datasets indicate the robustness and superiority of the proposed methods in both, the estimation of the annotator's reliability, and the assignment of actual labels, against the state-of-the-art algorithms and the simple majority voting.
Multimodal learning helps to comprehensively understand the world, by integrating different senses. Accordingly, multiple input modalities are expected to boost model performance, but we actually find that they are not fully exploited even when the multimodal model outperforms its uni-modal counterpart. Specifically, in this paper we point out that existing multimodal discriminative models, in which uniform objective is designed for all modalities, could remain under-optimized uni-modal representations, caused by another dominated modality in some scenarios, e.g., sound in blowing wind event, vision in drawing picture event, etc. To alleviate this optimization imbalance, we propose on-the-fly gradient modulation to adaptively control the optimization of each modality, via monitoring the discrepancy of their contribution towards the learning objective. Further, an extra Gaussian noise that changes dynamically is introduced to avoid possible generalization drop caused by gradient modulation. As a result, we achieve considerable improvement over common fusion methods on different multimodal tasks, and this simple strategy can also boost existing multimodal methods, which illustrates its efficacy and versatility. The source code is available at \url{//github.com/GeWu-Lab/OGM-GE_CVPR2022}.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success and become a milestone in the field of artificial intelligence (AI). Owing to sophisticated pre-training objectives and huge model parameters, large-scale PTMs can effectively capture knowledge from massive labeled and unlabeled data. By storing knowledge into huge parameters and fine-tuning on specific tasks, the rich knowledge implicitly encoded in huge parameters can benefit a variety of downstream tasks, which has been extensively demonstrated via experimental verification and empirical analysis. It is now the consensus of the AI community to adopt PTMs as backbone for downstream tasks rather than learning models from scratch. In this paper, we take a deep look into the history of pre-training, especially its special relation with transfer learning and self-supervised learning, to reveal the crucial position of PTMs in the AI development spectrum. Further, we comprehensively review the latest breakthroughs of PTMs. These breakthroughs are driven by the surge of computational power and the increasing availability of data, towards four important directions: designing effective architectures, utilizing rich contexts, improving computational efficiency, and conducting interpretation and theoretical analysis. Finally, we discuss a series of open problems and research directions of PTMs, and hope our view can inspire and advance the future study of PTMs.
Deep learning has revolutionized speech recognition, image recognition, and natural language processing since 2010, each involving a single modality in the input signal. However, many applications in artificial intelligence involve more than one modality. It is therefore of broad interest to study the more difficult and complex problem of modeling and learning across multiple modalities. In this paper, a technical review of the models and learning methods for multimodal intelligence is provided. The main focus is the combination of vision and natural language, which has become an important area in both computer vision and natural language processing research communities. This review provides a comprehensive analysis of recent work on multimodal deep learning from three new angles - learning multimodal representations, the fusion of multimodal signals at various levels, and multimodal applications. On multimodal representation learning, we review the key concept of embedding, which unifies the multimodal signals into the same vector space and thus enables cross-modality signal processing. We also review the properties of the many types of embedding constructed and learned for general downstream tasks. On multimodal fusion, this review focuses on special architectures for the integration of the representation of unimodal signals for a particular task. On applications, selected areas of a broad interest in current literature are covered, including caption generation, text-to-image generation, and visual question answering. We believe this review can facilitate future studies in the emerging field of multimodal intelligence for the community.
Multi-view networks are ubiquitous in real-world applications. In order to extract knowledge or business value, it is of interest to transform such networks into representations that are easily machine-actionable. Meanwhile, network embedding has emerged as an effective approach to generate distributed network representations. Therefore, we are motivated to study the problem of multi-view network embedding, with a focus on the characteristics that are specific and important in embedding this type of networks. In our practice of embedding real-world multi-view networks, we identify two such characteristics, which we refer to as preservation and collaboration. We then explore the feasibility of achieving better embedding quality by simultaneously modeling preservation and collaboration, and propose the mvn2vec algorithms. With experiments on a series of synthetic datasets, an internal Snapchat dataset, and two public datasets, we further confirm the presence and importance of preservation and collaboration. These experiments also demonstrate that better embedding can be obtained by simultaneously modeling the two characteristics, while not over-complicating the model or requiring additional supervision.
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