Successor Feature Sets: Generalizing Successor Representations Across Policies

Successor-style representations have many advantages for reinforcement learning: for example, they can help an agent generalize from past experience to new goals, and they have been proposed as explanations of behavioral and neural data from human and animal learners. They also form a natural bridge between model-based and model-free RL methods: like the former they make predictions about future experiences, and like the latter they allow efficient prediction of total discounted rewards. However, successor-style representations are not optimized to generalize across policies: typically, we maintain a limited-length list of policies, and share information among them by representation learning or GPI. Successor-style representations also typically make no provision for gathering information or reasoning about latent variables. To address these limitations, we bring together ideas from predictive state representations, belief space value iteration, successor features, and convex analysis: we develop a new, general successor-style representation, together with a Bellman equation that connects multiple sources of information within this representation, including different latent states, policies, and reward functions. The new representation is highly expressive: for example, it lets us efficiently read off an optimal policy for a new reward function, or a policy that imitates a new demonstration. For this paper, we focus on exact computation of the new representation in small, known environments, since even this restricted setting offers plenty of interesting questions. Our implementation does not scale to large, unknown environments -- nor would we expect it to, since it generalizes POMDP value iteration, which is difficult to scale. However, we believe that future work will allow us to extend our ideas to approximate reasoning in large, unknown environments.

Understanding and Mitigating Accuracy Disparity in Regression

With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity on prediction accuracy between different demographic subgroups has called for fundamental understanding on the source of such disparity and algorithmic intervention to mitigate it. In this paper, we study the accuracy disparity problem in regression. To begin with, we first propose an error decomposition theorem, which decomposes the accuracy disparity into the distance between marginal label distributions and the distance between conditional representations, to help explain why such accuracy disparity appears in practice. Motivated by this error decomposition and the general idea of distribution alignment with statistical distances, we then propose an algorithm to reduce this disparity, and analyze its game-theoretic optima of the proposed objective functions. To corroborate our theoretical findings, we also conduct experiments on five benchmark datasets. The experimental results suggest that our proposed algorithms can effectively mitigate accuracy disparity while maintaining the predictive power of the regression models.

Fundamental Limits and Tradeoffs in Invariant Representation Learning

Many machine learning applications involve learning representations that achieve two competing goals: To maximize information or accuracy with respect to a subset of features (e.g.\ for prediction) while simultaneously maximizing invariance or independence with respect to another, potentially overlapping, subset of features (e.g.\ for fairness, privacy, etc). Typical examples include privacy-preserving learning, domain adaptation, and algorithmic fairness, just to name a few. In fact, all of the above problems admit a common minimax game-theoretic formulation, whose equilibrium represents a fundamental tradeoff between accuracy and invariance. Despite its abundant applications in the aforementioned domains, theoretical understanding on the limits and tradeoffs of invariant representations is severely lacking. In this paper, we provide an information-theoretic analysis of this general and important problem under both classification and regression settings. In both cases, we analyze the inherent tradeoffs between accuracy and invariance by providing a geometric characterization of the feasible region in the information plane, where we connect the geometric properties of this feasible region to the fundamental limitations of the tradeoff problem. In the regression setting, we also derive a tight lower bound on the Lagrangian objective that quantifies the tradeoff between accuracy and invariance. This lower bound leads to a better understanding of the tradeoff via the spectral properties of the joint distribution. In both cases, our results shed new light on this fundamental problem by providing insights on the interplay between accuracy and invariance. These results deepen our understanding of this fundamental problem and may be useful in guiding the design of adversarial representation learning algorithms.

An Empirical Investigation of Beam-Aware Training in Supertagging

Structured prediction is often approached by training a locally normalized model with maximum likelihood and decoding approximately with beam search. This approach leads to mismatches as, during training, the model is not exposed to its mistakes and does not use beam search. Beam-aware training aims to address these problems, but unfortunately, it is not yet widely used due to a lack of understanding about how it impacts performance, when it is most useful, and whether it is stable. Recently, Negrinho et al. (2018) proposed a meta-algorithm that captures beam-aware training algorithms and suggests new ones, but unfortunately did not provide empirical results. In this paper, we begin an empirical investigation: we train the supertagging model of Vaswani et al. (2016) and a simpler model with instantiations of the meta-algorithm. We explore the influence of various design choices and make recommendations for choosing them. We observe that beam-aware training improves performance for both models, with large improvements for the simpler model which must effectively manage uncertainty during decoding. Our results suggest that a model must be learned with search to maximize its effectiveness.

Conditional Learning of Fair Representations

We propose a novel algorithm for learning fair representations that can simultaneously mitigate two notions of disparity among different demographic subgroups. Two key components underpinning the design of our algorithm are balanced error rate and conditional alignment of representations. We show how these two components contribute to ensuring accuracy parity and equalized false-positive and false-negative rates across groups without impacting demographic parity. Furthermore, we also demonstrate both in theory and on two real-world experiments that the proposed algorithm leads to a better utility-fairness trade-off on balanced datasets compared with existing algorithms on learning fair representations.

Learning Neural Networks with Adaptive Regularization

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes method. Specifically, we propose to construct a matrix-variate normal prior (on weights) whose covariance matrix has a Kronecker product structure. This structure is designed to capture the correlations in neurons through backpropagation. Under the assumption of this Kronecker factorization, the prior encourages neurons to borrow statistical strength from one another. Hence, it leads to an adaptive and data-dependent regularization when training networks on small datasets. To optimize the model, we present an efficient block coordinate descent algorithm with analytical solutions. Empirically, we demonstrate that the proposed method helps networks converge to local optima with smaller stable ranks and spectral norms. These properties suggest better generalizations and we present empirical results to support this expectation. We also verify the effectiveness of the approach on multiclass classification and multitask regression problems with various network structures.

Inherent Tradeoffs in Learning Fair Representation

With the prevalence of machine learning in high-stakes applications, especially the ones regulated by anti-discrimination laws or societal norms, it is crucial to ensure that the predictive models do not propagate any existing bias or discrimination. Due to the ability of deep neural nets to learn rich representations, recent advances in algorithmic fairness have focused on learning fair representations with adversarial techniques to reduce bias in data while preserving utility simultaneously. In this paper, through the lens of information theory, we provide the first result that quantitatively characterizes the tradeoff between demographic parity and the joint utility across different population groups. Specifically, when the base rates differ between groups, we show that any method aiming to learn fair representation admits an information-theoretic lower bound on the joint error across these groups. To complement our negative results, we also prove that if the optimal decision functions across different groups are close, then learning fair representation leads to an alternative notion of fairness, known as the accuracy parity, which states that the error rates are close between groups. Our theoretical findings are also confirmed empirically on real-world datasets. We believe our insights contribute to better understanding of the tradeoff between utility and different notions of fairness.

Adversarial Task-Specific Privacy Preservation under Attribute Attack

With the prevalence of machine learning services, crowdsourced data containing sensitive information poses substantial privacy challenges. Existing works focusing on protecting against membership inference attacks under the rigorous notion of differential privacy are susceptible to attribute inference attacks. In this paper, we develop a theoretical framework for task-specific privacy under the attack of attribute inference. Under our framework, we propose a minimax optimization formulation with a practical algorithm to protect a given attribute and preserve utility. We also extend our formulation so that multiple attributes could be simultaneously protected. Theoretically, we prove an information-theoretic lower bound to characterize the inherent tradeoff between utility and privacy when they are correlated. Empirically, we conduct experiments with real-world tasks that demonstrate the effectiveness of our method compared with state-of-the-art baseline approaches.

On Learning Invariant Representation for Domain Adaptation

Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the learnt representation, together with the hypothesis learnt from the source domain, can generalize to the target domain. In this paper, we first construct a simple counterexample showing that, contrary to common belief, the above conditions are not sufficient to guarantee successful domain adaptation. In particular, the counterexample (Fig. 1) exhibits \emph{conditional shift}: the class-conditional distributions of input features change between source and target domains. To give a sufficient condition for domain adaptation, we propose a natural and interpretable generalization upper bound that explicitly takes into account the aforementioned shift. Moreover, we shed new light on the problem by proving an information-theoretic lower bound on the joint error of \emph{any} domain adaptation method that attempts to learn invariant representations. Our result characterizes a fundamental tradeoff between learning invariant representations and achieving small joint error on both domains when the marginal label distributions differ from source to target. Finally, we conduct experiments on real-world datasets that corroborate our theoretical findings. We believe these insights are helpful in guiding the future design of domain adaptation and representation learning algorithms.