We consider the problem of minimizing a smooth convex function by reducing the optimization to computing the Nash equilibrium of a particular zero-sum convex-concave game. Zero-sum games can be solved using online learning dynamics, where a classical technique involves simulating two no-regret algorithms that play against each other and, after $T$ rounds, the average iterate is guaranteed to solve the original optimization problem with error decaying as $O(\log T/T)$. In this paper we show that the technique can be enhanced to a rate of $O(1/T^2)$ by extending recent work \cite{RS13,SALS15} that leverages \textit{optimistic learning} to speed up equilibrium computation. The resulting optimization algorithm derived from this analysis coincides \textit{exactly} with the well-known \NA \cite{N83a} method, and indeed the same story allows us to recover several variants of the Nesterov's algorithm via small tweaks. We are also able to establish the accelerated linear rate for a function which is both strongly-convex and smooth. This methodology unifies a number of different iterative optimization methods: we show that the \HB algorithm is precisely the non-optimistic variant of \NA, and recent prior work already established a similar perspective on \FW \cite{AW17,ALLW18}.

We address the problem of learning accurate 3D shape and camera pose from a collection of unlabeled category-specific images. We train a convolutional network to predict both the shape and the pose from a single image by minimizing the reprojection error: given several views of an object, the projections of the predicted shapes to the predicted camera poses should match the provided views. To deal with pose ambiguity, we introduce an ensemble of pose predictors which we then distill to a single "student" model. To allow for efficient learning of high-fidelity shapes, we represent the shapes by point clouds and devise a formulation allowing for differentiable projection of these. Our experiments show that the distilled ensemble of pose predictors learns to estimate the pose accurately, while the point cloud representation allows to predict detailed shape models.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of $\epsilon$, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than $1/L$, then the query complexity is on the order of $L\log(1/\epsilon)$ as $\epsilon \to 0$. Our result demonstrates that increased privacy, as captured by $L$, comes at the expense of a \emph{multiplicative} increase in query complexity. The proof builds on Fano's inequality and properties of certain proportional-sampling estimators.

Recently, learning discriminative features to improve the recognition performances gradually becomes the primary goal of deep learning, and numerous remarkable works have emerged. In this paper, we propose a novel yet extremely simple method Virtual Softmax to enhance the discriminative property of learned features by injecting a dynamic virtual negative class into the original softmax. Injecting virtual class aims to enlarge inter-class margin and compress intra-class distribution by strengthening the decision boundary constraint. Although it seems weird to optimize with this additional virtual class, we show that our method derives from an intuitive and clear motivation, and it indeed encourages the features to be more compact and separable. This paper empirically and experimentally demonstrates the superiority of Virtual Softmax, improving the performances on a variety of object classification and face verification tasks.

In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an $O(\sqrt{T}(1+P_T))$ dynamic regret, where $T$ is the number of iterations and $P_T$ is the path-length of the comparator sequence. However, this result is unsatisfactory, as there exists a large gap from the $\Omega(\sqrt{T(1+P_T)})$ lower bound established in our paper. To address this limitation, we develop a novel online method, namely adaptive learning for dynamic environment (Ader), which achieves an optimal $O(\sqrt{T(1+P_T)})$ dynamic regret. The basic idea is to maintain a set of experts, each attaining an optimal dynamic regret for a specific path-length, and combines them with an expert-tracking algorithm. Furthermore, we propose an improved Ader based on the surrogate loss, and in this way the number of gradient evaluations per round is reduced from $O(\log T)$ to $1$. Finally, we extend Ader to the setting that a sequence of dynamical models is available to characterize the comparators.

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise is to optimize a proxy objective that minimizes a weighted linear combination of per-task losses. However, this workaround is only valid when the tasks do not compete, which is rarely the case. In this paper, we explicitly cast multi-task learning as multi-objective optimization, with the overall objective of finding a Pareto optimal solution. To this end, we use algorithms developed in the gradient-based multi-objective optimization literature. These algorithms are not directly applicable to large-scale learning problems since they scale poorly with the dimensionality of the gradients and the number of tasks. We therefore propose an upper bound for the multi-objective loss and show that it can be optimized efficiently. We further prove that optimizing this upper bound yields a Pareto optimal solution under realistic assumptions. We apply our method to a variety of multi-task deep learning problems including digit classification, scene understanding (joint semantic segmentation, instance segmentation, and depth estimation), and multi-label classification. Our method produces higher-performing models than recent multi-task learning formulations or per-task training.

Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence cannot be tested in data and can invalidate any causal conclusion. Experimental data does not suffer from confounding but is usually limited in both scope and scale. We introduce a novel method of using limited experimental data to correct the hidden confounding in causal effect models trained on larger observational data, even if the observational data does not fully overlap with the experimental data. Our method makes strictly weaker assumptions than existing approaches, and we prove conditions under which it yields a consistent estimator. We demonstrate our method's efficacy using real-world data from a large educational experiment.

In many real-world learning tasks, it is hard to directly optimize the true performance measures, meanwhile choosing the right surrogate objectives is also difficult. Under this situation, it is desirable to incorporate an optimization of objective process into the learning loop based on weak modeling of the relationship between the true measure and the objective. In this work, we discuss the task of objective adaptation, in which the learner iteratively adapts the learning objective to the underlying true objective based on the preference feedback from an oracle. We show that when the objective can be linearly parameterized, this preference based learning problem can be solved by utilizing the dueling bandit model. A novel sampling based algorithm DL^2M is proposed to learn the optimal parameter, which enjoys strong theoretical guarantees and efficient empirical performance. To avoid learning a hypothesis from scratch after each objective function update, a boosting based hypothesis adaptation approach is proposed to efficiently adapt any pre-learned element hypothesis to the current objective. We apply the overall approach to multi-label learning, and show that the proposed approach achieves significant performance under various multi-label performance measures.

In this paper, we propose a conceptually simple and general framework called MetaGAN for few-shot learning problems. Most state-of-the-art few-shot classification models can be integrated with MetaGAN in a principled and straightforward way. By introducing an adversarial generator conditioned on tasks, we augment vanilla few-shot classification models with the ability to discriminate between real and fake data. We argue that this GAN-based approach can help few-shot classifiers to learn sharper decision boundary, which could generalize better. We show that with our MetaGAN framework, we can extend supervised few-shot learning models to naturally cope with unsupervised data. Different from previous work in semi-supervised few-shot learning, our algorithms can deal with semi-supervision at both sample-level and task-level. We give theoretical justifications of the strength of MetaGAN, and validate the effectiveness of MetaGAN on challenging few-shot image classification benchmarks.

Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework (Sutton et al., 1999). However, only recently in (Bacon et al., 2017) was a policy gradient theorem derived for online learning of general purpose options in an end to end fashion. In this work, we extend previous work on this topic that only focuses on learning a two-level hierarchy including options and primitive actions to enable learning simultaneously at multiple resolutions in time. We achieve this by considering an arbitrarily deep hierarchy of options where high level temporally extended options are composed of lower level options with finer resolutions in time. We extend results from (Bacon et al., 2017) and derive policy gradient theorems for a deep hierarchy of options. Our proposed hierarchical option-critic architecture is capable of learning internal policies, termination conditions, and hierarchical compositions over options without the need for any intrinsic rewards or subgoals. Our empirical results in both discrete and continuous environments demonstrate the efficiency of our framework.