We use functional mirror ascent to propose a general framework (referred to as FMA-PG) for designing policy gradient methods. The functional perspective distinguishes between a policys functional representation (what are its sufficient statistics) an
d its parameterization (how are these statistics represented) and naturally results in computationally efficient off-policy updates. For simple policy parameterizations, the FMA-PG framework ensures that the optimal policy is a fixed point of the updates. It also allows us to handle complex policy parameterizations (e.g., neural networks) while guaranteeing policy improvement. Our framework unifies several PG methods and opens the way for designing sample-efficient variants of existing methods. Moreover, it recovers important implementation heuristics (e.g., using forward vs reverse KL divergence) in a principled way. With a softmax functional representation, FMA-PG results in a variant of TRPO with additional desirable properties. It also suggests an improved variant of PPO, whose robustness and efficiency we empirically demonstrate on MuJoCo. Via experiments on simple reinforcement learning problems, we evaluate algorithms instantiated by FMA-PG.
In self-supervised visual representation learning, a feature extractor is trained on a pretext task for which labels can be generated cheaply, without human annotation. A central challenge in this approach is that the feature extractor quickly learns
to exploit low-level visual features such as color aberrations or watermarks and then fails to learn useful semantic representations. Much work has gone into identifying such shortcut features and hand-designing schemes to reduce their effect. Here, we propose a general framework for mitigating the effect shortcut features. Our key assumption is that those features which are the first to be exploited for solving the pretext task may also be the most vulnerable to an adversary trained to make the task harder. We show that this assumption holds across common pretext tasks and datasets by training a lens network to make small image changes that maximally reduce performance in the pretext task. Representations learned with the modified images outperform those learned without in all tested cases. Additionally, the modifications made by the lens reveal how the choice of pretext task and dataset affects the features learned by self-supervision.
Learning useful representations with little or no supervision is a key challenge in artificial intelligence. We provide an in-depth review of recent advances in representation learning with a focus on autoencoder-based models. To organize these resul
ts we make use of meta-priors believed useful for downstream tasks, such as disentanglement and hierarchical organization of features. In particular, we uncover three main mechanisms to enforce such properties, namely (i) regularizing the (approximate or aggregate) posterior distribution, (ii) factorizing the encoding and decoding distribution, or (iii) introducing a structured prior distribution. While there are some promising results, implicit or explicit supervision remains a key enabler and all current methods use strong inductive biases and modeling assumptions. Finally, we provide an analysis of autoencoder-based representation learning through the lens of rate-distortion theory and identify a clear tradeoff between the amount of prior knowledge available about the downstream tasks, and how useful the representation is for this task.
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset constructio
n for machine learning. In Section 2, we present both the intuition behind and a theoretically sound framework to construct coresets for general problems and apply it to $k$-means clustering. In Section 3 we summarize existing coreset construction algorithms for a variety of machine learning problems such as maximum likelihood estimation of mixture models, Bayesian non-parametric models, principal component analysis, regression and general empirical risk minimization.
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances that can fit
in memory - must grow with the data set size. In practice, while one can provision many machines, the capacity of each machine is limited by physical constraints. We propose a truly scalable approach for distributed submodular maximization under fixed capacity. The proposed framework applies to a broad class of algorithms and constraints and provides theoretical guarantees on the approximation factor for any available capacity. We empirically evaluate the proposed algorithm on a variety of data sets and demonstrate that it achieves performance competitive with the centralized greedy solution.
Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling these tech
niques to massive data sets without sacrificing accuracy is a challenging task. We propose a novel algorithm based on the intuition that outliers have a significant influence on the quality of divergence-based clustering solutions. We propose sensitivity - the worst-case impact of a data point on the clustering objective - as a measure of outlierness. We then prove that influence, a (non-trivial) upper-bound on the sensitivity, can be computed by a simple linear time algorithm. To scale beyond a single machine, we propose a communication efficient distributed algorithm. In an extensive experimental evaluation, we demonstrate the effectiveness and establish the statistical significance of the proposed approach. In particular, it outperforms the most popular distance-based approaches while being several orders of magnitude faster.
Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means
and Gaussian mixture models to massive data sets. However, until now, the algorithms and the corresponding theory were usually specific to each clustering problem. We propose a single, practical algorithm to construct strong coresets for a large class of hard and soft clustering problems based on Bregman divergences. This class includes hard clustering with popular distortion measures such as the Squared Euclidean distance, the Mahalanobis distance, KL-divergence and Itakura-Saito distance. The corresponding soft clustering problems are directly related to popular mixture models due to a dual relationship between Bregman divergences and Exponential family distributions. Our theoretical results further imply a randomized polynomial-time approximation scheme for hard clustering. We demonstrate the practicality of the proposed algorithm in an empirical evaluation.
