arXiv subjects

Tengyu Ma

Publications and source records attributed to Tengyu Ma.

At least 91 records · Page 5Linked to original sources

arXiv2021

Active Online Learning with Hidden Shifting Domains

Online machine learning systems need to adapt to domain shifts. Meanwhile, acquiring label at every timestep is expensive. We propose a surprisingly simple algorithm that adaptively balances its regret and its number of label queries in settings where the data streams are from a mixture of hidden domains. For online linear regression with oblivious adversaries, we provide a tight tradeoff that depends on the durations and dimensionalities of the hidden domains. Our algorithm can adaptively deal with interleaving spans of inputs from different domains. We also generalize our results to non-linear regression for hypothesis classes with bounded eluder dimension and adaptive adversaries. Experiments on synthetic and realistic datasets demonstrate that our algorithm achieves lower regret than uniform queries and greedy queries with equal labeling budget.

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arXiv2021

Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guarantees

Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper introduces a novel algorithmic framework for designing and analyzing model-based RL algorithms with theoretical guarantees. We design a meta-algorithm with a theoretical guarantee of monotone improvement to a local maximum of the expected reward. The meta-algorithm iteratively builds a lower bound of the expected reward based on the estimated dynamical model and sample trajectories, and then maximizes the lower bound jointly over the policy and the model. The framework extends the optimism-in-face-of-uncertainty principle to non-linear dynamical models in a way that requires \textit{no explicit} uncertainty quantification. Instantiating our framework with simplification gives a variant of model-based RL algorithms Stochastic Lower Bounds Optimization (SLBO). Experiments demonstrate that SLBO achieves state-of-the-art performance when only one million or fewer samples are permitted on a range of continuous control benchmark tasks.

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arXiv2020

Document-Level Relation Extraction with Adaptive Thresholding and Localized Context Pooling

Document-level relation extraction (RE) poses new challenges compared to its sentence-level counterpart. One document commonly contains multiple entity pairs, and one entity pair occurs multiple times in the document associated with multiple possible relations. In this paper, we propose two novel techniques, adaptive thresholding and localized context pooling, to solve the multi-label and multi-entity problems. The adaptive thresholding replaces the global threshold for multi-label classification in the prior work with a learnable entities-dependent threshold. The localized context pooling directly transfers attention from pre-trained language models to locate relevant context that is useful to decide the relation. We experiment on three document-level RE benchmark datasets: DocRED, a recently released large-scale RE dataset, and two datasets CDRand GDA in the biomedical domain. Our ATLOP (Adaptive Thresholding and Localized cOntext Pooling) model achieves an F1 score of 63.4, and also significantly outperforms existing models on both CDR and GDA.

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arXiv2020

Self-training Avoids Using Spurious Features Under Domain Shift

In unsupervised domain adaptation, existing theory focuses on situations where the source and target domains are close. In practice, conditional entropy minimization and pseudo-labeling work even when the domain shifts are much larger than those analyzed by existing theory. We identify and analyze one particular setting where the domain shift can be large, but these algorithms provably work: certain spurious features correlate with the label in the source domain but are independent of the label in the target. Our analysis considers linear classification where the spurious features are Gaussian and the non-spurious features are a mixture of log-concave distributions. For this setting, we prove that entropy minimization on unlabeled target data will avoid using the spurious feature if initialized with a decently accurate source classifier, even though the objective is non-convex and contains multiple bad local minima using the spurious features. We verify our theory for spurious domain shift tasks on semi-synthetic Celeb-A and MNIST datasets. Our results suggest that practitioners collect and self-train on large, diverse datasets to reduce biases in classifiers even if labeling is impractical.

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arXiv2020

MOPO: Model-based Offline Policy Optimization

Offline reinforcement learning (RL) refers to the problem of learning policies entirely from a large batch of previously collected data. This problem setting offers the promise of utilizing such datasets to acquire policies without any costly or dangerous active exploration. However, it is also challenging, due to the distributional shift between the offline training data and those states visited by the learned policy. Despite significant recent progress, the most successful prior methods are model-free and constrain the policy to the support of data, precluding generalization to unseen states. In this paper, we first observe that an existing model-based RL algorithm already produces significant gains in the offline setting compared to model-free approaches. However, standard model-based RL methods, designed for the online setting, do not provide an explicit mechanism to avoid the offline setting's distributional shift issue. Instead, we propose to modify the existing model-based RL methods by applying them with rewards artificially penalized by the uncertainty of the dynamics. We theoretically show that the algorithm maximizes a lower bound of the policy's return under the true MDP. We also characterize the trade-off between the gain and risk of leaving the support of the batch data. Our algorithm, Model-based Offline Policy Optimization (MOPO), outperforms standard model-based RL algorithms and prior state-of-the-art model-free offline RL algorithms on existing offline RL benchmarks and two challenging continuous control tasks that require generalizing from data collected for a different task. The code is available at https://github.com/tianheyu927/mopo.

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arXiv2020

Meta-learning Transferable Representations with a Single Target Domain

Recent works found that fine-tuning and joint training---two popular approaches for transfer learning---do not always improve accuracy on downstream tasks. First, we aim to understand more about when and why fine-tuning and joint training can be suboptimal or even harmful for transfer learning. We design semi-synthetic datasets where the source task can be solved by either source-specific features or transferable features. We observe that (1) pre-training may not have incentive to learn transferable features and (2) joint training may simultaneously learn source-specific features and overfit to the target. Second, to improve over fine-tuning and joint training, we propose Meta Representation Learning (MeRLin) to learn transferable features. MeRLin meta-learns representations by ensuring that a head fit on top of the representations with target training data also performs well on target validation data. We also prove that MeRLin recovers the target ground-truth model with a quadratic neural net parameterization and a source distribution that contains both transferable and source-specific features. On the same distribution, pre-training and joint training provably fail to learn transferable features. MeRLin empirically outperforms previous state-of-the-art transfer learning algorithms on various real-world vision and NLP transfer learning benchmarks.

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arXiv2020

Beyond Lazy Training for Over-parameterized Tensor Decomposition

Over-parametrization is an important technique in training neural networks. In both theory and practice, training a larger network allows the optimization algorithm to avoid bad local optimal solutions. In this paper we study a closely related tensor decomposition problem: given an $l$-th order tensor in $(R^d)^{\otimes l}$ of rank $r$ (where $r\ll d$), can variants of gradient descent find a rank $m$ decomposition where $m > r$? We show that in a lazy training regime (similar to the NTK regime for neural networks) one needs at least $m = Ω(d^{l-1})$, while a variant of gradient descent can find an approximate tensor when $m = O^*(r^{2.5l}\log d)$. Our results show that gradient descent on over-parametrized objective could go beyond the lazy training regime and utilize certain low-rank structure in the data.

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arXiv2020

The Implicit and Explicit Regularization Effects of Dropout

Dropout is a widely-used regularization technique, often required to obtain state-of-the-art for a number of architectures. This work demonstrates that dropout introduces two distinct but entangled regularization effects: an explicit effect (also studied in prior work) which occurs since dropout modifies the expected training objective, and, perhaps surprisingly, an additional implicit effect from the stochasticity in the dropout training update. This implicit regularization effect is analogous to the effect of stochasticity in small mini-batch stochastic gradient descent. We disentangle these two effects through controlled experiments. We then derive analytic simplifications which characterize each effect in terms of the derivatives of the model and the loss, for deep neural networks. We demonstrate these simplified, analytic regularizers accurately capture the important aspects of dropout, showing they faithfully replace dropout in practice.

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arXiv2020

Individual Calibration with Randomized Forecasting

Machine learning applications often require calibrated predictions, e.g. a 90\% credible interval should contain the true outcome 90\% of the times. However, typical definitions of calibration only require this to hold on average, and offer no guarantees on predictions made on individual samples. Thus, predictions can be systematically over or under confident on certain subgroups, leading to issues of fairness and potential vulnerabilities. We show that calibration for individual samples is possible in the regression setup if the predictions are randomized, i.e. outputting randomized credible intervals. Randomization removes systematic bias by trading off bias with variance. We design a training objective to enforce individual calibration and use it to train randomized regression functions. The resulting models are more calibrated for arbitrarily chosen subgroups of the data, and can achieve higher utility in decision making against adversaries that exploit miscalibrated predictions.

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arXiv2020

On the Expressivity of Neural Networks for Deep Reinforcement Learning

We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, $Q$-functions, and dynamics. We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal $Q$-functions and policies are much more complex than the dynamics. We hypothesize many real-world MDPs also have a similar property. For these MDPs, model-based planning is a favorable algorithm, because the resulting policies can approximate the optimal policy significantly better than a neural network parameterization can, and model-free or model-based policy optimization rely on policy parameterization. Motivated by the theory, we apply a simple multi-step model-based bootstrapping planner (BOOTS) to bootstrap a weak $Q$-function into a stronger policy. Empirical results show that applying BOOTS on top of model-based or model-free policy optimization algorithms at the test time improves the performance on MuJoCo benchmark tasks.

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arXiv2020

Entity and Evidence Guided Relation Extraction for DocRED

Document-level relation extraction is a challenging task which requires reasoning over multiple sentences in order to predict relations in a document. In this paper, we pro-pose a joint training frameworkE2GRE(Entity and Evidence Guided Relation Extraction)for this task. First, we introduce entity-guided sequences as inputs to a pre-trained language model (e.g. BERT, RoBERTa). These entity-guided sequences help a pre-trained language model (LM) to focus on areas of the document related to the entity. Secondly, we guide the fine-tuning of the pre-trained language model by using its internal attention probabilities as additional features for evidence prediction.Our new approach encourages the pre-trained language model to focus on the entities and supporting/evidence sentences. We evaluate our E2GRE approach on DocRED, a recently released large-scale dataset for relation extraction. Our approach is able to achieve state-of-the-art results on the public leaderboard across all metrics, showing that our E2GRE is both effective and synergistic on relation extraction and evidence prediction.

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arXiv2020

Learning Over-Parametrized Two-Layer ReLU Neural Networks beyond NTK

We consider the dynamic of gradient descent for learning a two-layer neural network. We assume the input $x\in\mathbb{R}^d$ is drawn from a Gaussian distribution and the label of $x$ satisfies $f^{\star}(x) = a^{\top}|W^{\star}x|$, where $a\in\mathbb{R}^d$ is a nonnegative vector and $W^{\star} \in\mathbb{R}^{d\times d}$ is an orthonormal matrix. We show that an over-parametrized two-layer neural network with ReLU activation, trained by gradient descent from random initialization, can provably learn the ground truth network with population loss at most $o(1/d)$ in polynomial time with polynomial samples. On the other hand, we prove that any kernel method, including Neural Tangent Kernel, with a polynomial number of samples in $d$, has population loss at least $Ω(1 / d)$.

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arXiv2020

Shape Matters: Understanding the Implicit Bias of the Noise Covariance

The noise in stochastic gradient descent (SGD) provides a crucial implicit regularization effect for training overparameterized models. Prior theoretical work largely focuses on spherical Gaussian noise, whereas empirical studies demonstrate the phenomenon that parameter-dependent noise -- induced by mini-batches or label perturbation -- is far more effective than Gaussian noise. This paper theoretically characterizes this phenomenon on a quadratically-parameterized model introduced by Vaskevicius et el. and Woodworth et el. We show that in an over-parameterized setting, SGD with label noise recovers the sparse ground-truth with an arbitrary initialization, whereas SGD with Gaussian noise or gradient descent overfits to dense solutions with large norms. Our analysis reveals that parameter-dependent noise introduces a bias towards local minima with smaller noise variance, whereas spherical Gaussian noise does not. Code for our project is publicly available.

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arXiv2020

Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel

Recent works have shown that on sufficiently over-parametrized neural nets, gradient descent with relatively large initialization optimizes a prediction function in the RKHS of the Neural Tangent Kernel (NTK). This analysis leads to global convergence results but does not work when there is a standard $\ell_2$ regularizer, which is useful to have in practice. We show that sample efficiency can indeed depend on the presence of the regularizer: we construct a simple distribution in d dimensions which the optimal regularized neural net learns with $O(d)$ samples but the NTK requires $Ω(d^2)$ samples to learn. To prove this, we establish two analysis tools: i) for multi-layer feedforward ReLU nets, we show that the global minimizer of a weakly-regularized cross-entropy loss is the max normalized margin solution among all neural nets, which generalizes well; ii) we develop a new technique for proving lower bounds for kernel methods, which relies on showing that the kernel cannot focus on informative features. Motivated by our generalization results, we study whether the regularized global optimum is attainable. We prove that for infinite-width two-layer nets, noisy gradient descent optimizes the regularized neural net loss to a global minimum in polynomial iterations.

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arXiv2020

Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks

Stochastic gradient descent with a large initial learning rate is widely used for training modern neural net architectures. Although a small initial learning rate allows for faster training and better test performance initially, the large learning rate achieves better generalization soon after the learning rate is annealed. Towards explaining this phenomenon, we devise a setting in which we can prove that a two layer network trained with large initial learning rate and annealing provably generalizes better than the same network trained with a small learning rate from the start. The key insight in our analysis is that the order of learning different types of patterns is crucial: because the small learning rate model first memorizes easy-to-generalize, hard-to-fit patterns, it generalizes worse on hard-to-generalize, easier-to-fit patterns than its large learning rate counterpart. This concept translates to a larger-scale setting: we demonstrate that one can add a small patch to CIFAR-10 images that is immediately memorizable by a model with small initial learning rate, but ignored by the model with large learning rate until after annealing. Our experiments show that this causes the small learning rate model's accuracy on unmodified images to suffer, as it relies too much on the patch early on.

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arXiv2020

Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentation

Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is unavoidable when no additional properties of the training data are considered. We suspect that this conundrum comes from the fact that these bounds depend on the training data only through the margin. In practice, many data-dependent techniques such as Batchnorm improve the generalization performance. For feedforward neural nets as well as RNNs, we obtain tighter Rademacher complexity bounds by considering additional data-dependent properties of the network: the norms of the hidden layers of the network, and the norms of the Jacobians of each layer with respect to all previous layers. Our bounds scale polynomially in depth when these empirical quantities are small, as is usually the case in practice. To obtain these bounds, we develop general tools for augmenting a sequence of functions to make their composition Lipschitz and then covering the augmented functions. Inspired by our theory, we directly regularize the network's Jacobians during training and empirically demonstrate that this improves test performance.

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arXiv2020

Robust and On-the-fly Dataset Denoising for Image Classification

Memorization in over-parameterized neural networks could severely hurt generalization in the presence of mislabeled examples. However, mislabeled examples are hard to avoid in extremely large datasets collected with weak supervision. We address this problem by reasoning counterfactually about the loss distribution of examples with uniform random labels had they were trained with the real examples, and use this information to remove noisy examples from the training set. First, we observe that examples with uniform random labels have higher losses when trained with stochastic gradient descent under large learning rates. Then, we propose to model the loss distribution of the counterfactual examples using only the network parameters, which is able to model such examples with remarkable success. Finally, we propose to remove examples whose loss exceeds a certain quantile of the modeled loss distribution. This leads to On-the-fly Data Denoising (ODD), a simple yet effective algorithm that is robust to mislabeled examples, while introducing almost zero computational overhead compared to standard training. ODD is able to achieve state-of-the-art results on a wide range of datasets including real-world ones such as WebVision and Clothing1M.

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arXiv2020

Understanding Self-Training for Gradual Domain Adaptation

Machine learning systems must adapt to data distributions that evolve over time, in applications ranging from sensor networks and self-driving car perception modules to brain-machine interfaces. We consider gradual domain adaptation, where the goal is to adapt an initial classifier trained on a source domain given only unlabeled data that shifts gradually in distribution towards a target domain. We prove the first non-vacuous upper bound on the error of self-training with gradual shifts, under settings where directly adapting to the target domain can result in unbounded error. The theoretical analysis leads to algorithmic insights, highlighting that regularization and label sharpening are essential even when we have infinite data, and suggesting that self-training works particularly well for shifts with small Wasserstein-infinity distance. Leveraging the gradual shift structure leads to higher accuracies on a rotating MNIST dataset and a realistic Portraits dataset.

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