We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all posterior distributions on an algorithm's random hyperparameters, including distributions that depend on the training data.

Transfer in reinforcement learning refers to the notion that generalization should occur not only within a task but also across tasks. We propose a transfer framework for the scenario where the reward function changes between tasks but the environment's dynamics remain the same. Our approach rests on two key ideas: successor features, a value function representation that decouples the dynamics of the environment from the rewards, and generalized policy improvement, a generalization of dynamic programming's policy improvement operation that considers a set of policies rather than a single one. Put together, the two ideas lead to an approach that integrates seamlessly within the reinforcement learning framework and allows the free exchange of information across tasks. The proposed method also provides performance guarantees for the transferred policy even before any learning has taken place. We derive two theorems that set our approach in firm theoretical ground and present experiments that show that it successfully promotes transfer in practice, significantly outperforming alternative methods in a sequence of navigation tasks and in the control of a simulated robotic arm.

Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user behavior. We propose a generalized click model that encompasses many existing models, including the position-based and cascade models. Our generalization motivates a novel online learning algorithm based on topological sort, which we call TopRank. TopRank is (a) more natural than existing algorithms, (b) has stronger regret guarantees than existing algorithms with comparable generality, (c) has a more insightful proof that leaves the door open to many generalizations, (d) outperforms existing algorithms empirically.

The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult, especially when the data distribution is presumed to be unknown. We show how a differentially private data-dependent prior yields a valid PAC-Bayes bound, and then show how non-private mechanisms for choosing priors can also yield generalization bounds. As an application of this result, we show that a Gaussian prior mean chosen via stochastic gradient Langevin dynamics (SGLD; Welling and Teh, 2011) leads to a valid PAC-Bayes bound due to control of the 2-Wasserstein distance to a differentially private stationary distribution. We study our data-dependent bounds empirically, and show that they can be nonvacuous even when other distribution-dependent bounds are vacuous.

Extreme multi-label classification (XMLC) is a problem of tagging an instance with a small subset of relevant labels chosen from an extremely large pool of possible labels. Large label spaces can be efficiently handled by organizing labels as a tree, like in the hierarchical softmax (HSM) approach commonly used for multi-class problems. In this paper, we investigate probabilistic label trees (PLTs) that have been recently devised for tackling XMLC problems. We show that PLTs are a no-regret multi-label generalization of HSM when precision@$k$ is used as a model evaluation metric. Critically, we prove that pick-one-label heuristic---a reduction technique from multi-label to multi-class that is routinely used along with HSM---is not consistent in general. We also show that our implementation of PLTs, referred to as extremeText (XT), obtains significantly better results than HSM with the pick-one-label heuristic and XML-CNN, a deep network specifically designed for XMLC problems. Moreover, XT is competitive to many state-of-the-art approaches in terms of statistical performance, model size and prediction time which makes it amenable to deploy in an online system.

While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of ---the common practice in which the choice of analysis depends on previous interactions with the same dataset. A recent line of work has introduced powerful, general purpose algorithms that ensure a property called (Cummings et al., COLT'16), which says that no person when given the output of the algorithm should be able to find any statistic for which the data differs significantly from the population it came from. In this work we show several limitations on the power of algorithms satisfying post hoc generalization. First, we show a tight lower bound on the error of any algorithm that satisfies post hoc generalization and answers adaptively chosen statistical queries, showing a strong barrier to progress in post selection data analysis. Second, we show that post hoc generalization is not closed under composition, despite many examples of such algorithms exhibiting strong composition properties.

While domain adaptation has been actively researched, most algorithms focus on the single-source-single-target adaptation setting. In this paper we propose new generalization bounds and algorithms under both classification and regression settings for unsupervised multiple source domain adaptation. Our theoretical analysis naturally leads to an efficient learning strategy using adversarial neural networks: we show how to interpret it as learning feature representations that are invariant to the multiple domain shifts while still being discriminative for the learning task. To this end, we propose multisource domain adversarial networks (MDAN) that approach domain adaptation by optimizing task-adaptive generalization bounds. To demonstrate the effectiveness of MDAN, we conduct extensive experiments showing superior adaptation performance on both classification and regression problems: sentiment analysis, digit classification, and vehicle counting.

Training models that generalize to new domains at test time is a problem of fundamental importance in machine learning.

It is commonly believed that an agent making decisions on behalf of two or more principals who have different utility functions should adopt a Pareto optimal policy, i.e. a policy that cannot be improved upon for one principal without making sacrifices for another. Harsanyi's theorem shows that when the principals have a common prior on the outcome distributions of all policies, a Pareto optimal policy for the agent is one that maximizes a fixed, weighted linear combination of the principals' utilities. In this paper, we derive a more precise generalization for the sequential decision setting in the case of principals with different priors on the dynamics of the environment. We refer to this generalization as the Negotiable Reinforcement Learning (NRL) framework. In this more general case, the relative weight given to each principal's utility should evolve over time according to how well the agent's observations conform with that principal's prior. To gain insight into the dynamics of this new framework, we implement a simple NRL agent and empirically examine its behavior in a simple environment.

In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models of images by probing the learning algorithm with carefully designed training datasets. By measuring properties of the learned distribution, we are able to find interesting patterns of generalization. We verify that these patterns are consistent across datasets, common models and architectures.