We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights using labeled source data and unlabeled target data, and then train a classifier on the weighted source samples. We derive a generalization bound for the classifier on the target domain which is independent of the (ambient) data dimensions, and instead only depends on the complexity of the function class. To the best of our knowledge, this is the first generalization bound for the label-shift problem where the labels in the target domain are not available. Based on this bound, we propose a regularized estimator for the small-sample regime which accounts for the uncertainty in the estimated weights. Experiments on the CIFAR-10 and MNIST datasets show that RLLS improves classification accuracy, especially in the low sample and large-shift regimes, compared to previous methods.
Precise near-ground trajectory control is difficult for multi-rotor drones, due to the complex aerodynamic effects caused by interactions between multi-rotor airflow and the environment. Conventional control methods often fail to properly account for these complex effects and fall short in accomplishing smooth landing. In this paper, we present a novel deep-learning-based robust nonlinear controller (Neural Lander) that improves control performance of a quadrotor during landing. Our approach combines a nominal dynamics model with a Deep Neural Network (DNN) that learns high-order interactions. We apply spectral normalization (SN) to constrain the Lipschitz constant of the DNN. Leveraging this Lipschitz property, we design a nonlinear feedback linearization controller using the learned model and prove system stability with disturbance rejection. To the best of our knowledge, this is the first DNN-based nonlinear feedback controller with stability guarantees that can utilize arbitrarily large neural nets. Experimental results demonstrate that the proposed controller significantly outperforms a Baseline Nonlinear Tracking Controller in both landing and cross-table trajectory tracking cases. We also empirically show that the DNN generalizes well to unseen data outside the training domain.
Sketching refers to a class of randomized dimensionality reduction methods that aim to preserve relevant information in large-scale datasets. They have efficient memory requirements and typically require just a single pass over the dataset. Efficient sketching methods have been derived for vector and matrix-valued datasets. When the datasets are higher-order tensors, a naive approach is to flatten the tensors into vectors or matrices and then sketch them. However, this is inefficient since it ignores the multi-dimensional nature of tensors. In this paper, we propose a novel multi-dimensional tensor sketch (MTS) that preserves higher order data structures while reducing dimensionality. We build this as an extension to the popular count sketch (CS) and show that it yields an unbiased estimator of the original tensor. We demonstrate significant advantages in compression ratios when the original data has decomposable tensor representations such as the Tucker, CP, tensor train or Kronecker product forms. We apply MTS to tensorized neural networks where we replace fully connected layers with tensor operations. We achieve nearly state of art accuracy with significant compression on image classification benchmarks.
We propose Generalized Trust Region Policy Optimization (GTRPO), a Reinforcement Learning algorithm for TRPO of Partially Observable Markov Decision Processes (POMDP). While the principle of policy gradient methods does not require any model assumption, previous studies of more sophisticated policy gradient methods are mainly limited to MDPs. Many real-world decision-making tasks, however, are inherently non-Markovian, i.e., only an incomplete representation of the environment is observable. Moreover, most of the advanced policy gradient methods are designed for infinite horizon MDPs. Our proposed algorithm, GTRPO, is a policy gradient method for continuous episodic POMDPs. We prove that its policy updates monotonically improve the expected cumulative return. We empirically study GTRPO on many RoboSchool environments, an extension to the MuJoCo environments, and provide insights into its empirical behavior.
Visual Question Answering (VQA) requires integration of feature maps with drastically different structures and focus of the correct regions. Image descriptors have structures at multiple spatial scales, while lexical inputs inherently follow a temporal sequence and naturally cluster into semantically different question types. A lot of previous works use complex models to extract feature representations but neglect to use high-level information summary such as question types in learning. In this work, we propose Question Type-guided Attention (QTA). It utilizes the information of question type to dynamically balance between bottom-up and top-down visual features, respectively extracted from ResNet and Faster R-CNN networks. We experiment with multiple VQA architectures with extensive input ablation studies over the TDIUC dataset and show that QTA systematically improves the performance by more than 5% across multiple question type categories such as "Activity Recognition", "Utility" and "Counting" on TDIUC dataset. By adding QTA on the state-of-art model MCB, we achieve 3% improvement for overall accuracy. Finally, we propose a multi-task extension to predict question types which generalizes QTA to applications that lack of question type, with minimal performance loss.
Reinforcement learning (RL) in Markov decision processes (MDPs) with large state spaces is a challenging problem. The performance of standard RL algorithms degrades drastically with the dimensionality of state space. However, in practice, these large MDPs typically incorporate a latent or hidden low-dimensional structure. In this paper, we study the setting of rich-observation Markov decision processes (ROMDP), where there are a small number of hidden states which possess an injective mapping to the observation states. In other words, every observation state is generated through a single hidden state, and this mapping is unknown a priori. We introduce a spectral decomposition method that consistently learns this mapping, and more importantly, achieves it with low regret. The estimated mapping is integrated into an optimistic RL algorithm (UCRL), which operates on the estimated hidden space. We derive finite-time regret bounds for our algorithm with a weak dependence on the dimensionality of the observed space. In fact, our algorithm asymptotically achieves the same average regret as the oracle UCRL algorithm, which has the knowledge of the mapping from hidden to observed spaces. Thus, we derive an efficient spectral RL algorithm for ROMDPs.
We propose Generative Adversarial Tree Search (GATS), a sample-efficient Deep Reinforcement Learning (DRL) algorithm. While Monte Carlo Tree Search (MCTS) is known to be effective for search and planning in RL, it is often sample-inefficient and therefore expensive to apply in practice. In this work, we develop a Generative Adversarial Network (GAN) architecture to model an environment's dynamics and a predictor model for the reward function. We exploit collected data from interaction with the environment to learn these models, which we then use for model-based planning. During planning, we deploy a finite depth MCTS, using the learned model for tree search and a learned Q-value for the leaves, to find the best action. We theoretically show that GATS improves the bias-variance trade-off in value-based DRL. Moreover, we show that the generative model learns the model dynamics using orders of magnitude fewer samples than the Q-learner. In non-stationary settings where the environment model changes, we find the generative model adapts significantly faster than the Q-learner to the new environment.
Unsupervised text embeddings extraction is crucial for text understanding in machine learning. Word2Vec and its variants have received substantial success in mapping words with similar syntactic or semantic meaning to vectors close to each other. However, extracting context-aware word-sequence embedding remains a challenging task. Training over large corpus is difficult as labels are difficult to get. More importantly, it is challenging for pre-trained models to obtain word-sequence embeddings that are universally good for all downstream tasks or for any new datasets. We propose a two-phased ConvDic+DeconvDec framework to solve the problem by combining a word-sequence dictionary learning model with a word-sequence embedding decode model. We propose a convolutional tensor decomposition mechanism to learn good word-sequence phrase dictionary in the learning phase. It is proved to be more accurate and much more efficient than the popular alternating minimization method. In the decode phase, we introduce a deconvolution framework that is immune to the problem of varying sentence lengths. The word-sequence embeddings we extracted using ConvDic+DeconvDec are universally good for a few downstream tasks we test on. The framework requires neither pre-training nor prior/outside information.
Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on large domains. This is because they mostly rely either on black-box function evaluations that do not capture the structure of the program, or on detailed execution traces that are expensive to obtain, and hence the training data has poor coverage of the domain under consideration. We present a novel framework that utilizes black-box function evaluations, in conjunction with symbolic expressions that define relationships between the given functions. We employ tree LSTMs to incorporate the structure of the symbolic expression trees. We use tree encoding for numbers present in function evaluation data, based on their decimal representation. We present an evaluation benchmark for this task to demonstrate our proposed model combines symbolic reasoning and function evaluation in a fruitful manner, obtaining high accuracies in our experiments. Our framework generalizes significantly better to expressions of higher depth and is able to fill partial equations with valid completions.