Combinatorial Bandits without Total Order for Arms

We consider the combinatorial bandits problem, where at each time step, the online learner selects a size-$k$ subset $s$ from the arms set $mathcal{A}$, where $left|mathcal{A}right| = n$, and observes a stochastic reward of each arm in the selected set $s$. The goal of the online learner is to minimize the regret, induced by not selecting $s^*$ which maximizes the expected total reward. Specifically, we focus on a challenging setting where 1) the reward distribution of an arm depends on the set $s$ it is part of, and crucially 2) there is textit{no total order} for the arms in $mathcal{A}$. In this paper, we formally present a reward model that captures set-dependent reward distribution and assumes no total order for arms. Correspondingly, we propose an Upper Confidence Bound (UCB) algorithm that maintains UCB for each individual arm and selects the arms with top-$k$ UCB. We develop a novel regret analysis and show an $Oleft(frac{k^2 n log T}{epsilon}right)$ gap-dependent regret bound as well as an $Oleft(k^2sqrt{n T log T}right)$ gap-independent regret bound. We also provide a lower bound for the proposed reward model, which shows our proposed algorithm is near-optimal for any constant $k$. Empirical results on various reward models demonstrate the broad applicability of our algorithm.

PECOS: Prediction for Enormous and Correlated Output Spaces

Many challenging problems in modern applications amount to finding relevant results from an enormous output space of potential candidates. The size of the output space for these problems can range from millions to billions. Moreover, training data is often limited for many of the so-called ``long-tail of items in the output space. Given the inherent paucity of training data for most of the items in the output space, developing machine learned models that perform well for spaces of this size is challenging. Fortunately, items in the output space are often correlated thereby presenting an opportunity to alleviate the data sparsity issue. In this paper, we propose the Prediction for Enormous and Correlated Output Spaces (PECOS) framework, a versatile and modular machine learning framework for solving prediction problems for very large output spaces, and apply it to the eXtreme Multilabel Ranking (XMR) problem: given an input instance, find and rank the most relevant items from an enormous but fixed and finite output space. PECOS is a three-phase framework: (i) in the first phase, PECOS organizes the output space using a semantic indexing scheme, (ii) in the second phase, PECOS uses the indexing to narrow down the output space by orders of magnitude using a machine learned matching scheme, and (iii) in the third phase, PECOS ranks the matched items using a final ranking scheme. The versatility and modularity of PECOS allows for easy plug-and-play of various choices for the indexing, matching, and ranking phases. On a dataset where the output space is of size 2.8 million, PECOS with a neural matcher results in a 10% increase in precision@1 (from 46% to 51.2%) over PECOS with a recursive linear matcher but takes 265x more time to train. We also develop fast real time inference procedures; for example, inference takes less than 10 milliseconds on the data set with 2.8 million labels.

Multiresolution Transformer Networks: Recurrence is Not Essential for Modeling Hierarchical Structure

The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in the input and the output, compared to the recurrent architectures. We establish connections between the dynamics in Transformer and recurrent networks to argue that several factors including gradient flow along an ensemble of multiple weakly dependent paths play a paramount role in the success of Transformer. We then leverage the dynamics to introduce {em Multiresolution Transformer Networks} as the first architecture that exploits hierarchical structure in data via self-attention. Our models significantly outperform state-of-the-art recurrent and hierarchical recurrent models on two real-world datasets for query suggestion, namely, aol and amazon. In particular, on AOL data, our model registers at least 20% improvement on each precision score, and over 25% improvement on the BLEU score with respect to the best performing recurrent model. We thus provide strong evidence that recurrence is not essential for modeling hierarchical structure.

AutoAssist: A Framework to Accelerate Training of Deep Neural Networks

Deep neural networks have yielded superior performance in many applications; however, the gradient computation in a deep model with millions of instances lead to a lengthy training process even with modern GPU/TPU hardware acceleration. In this paper, we propose AutoAssist, a simple framework to accelerate training of a deep neural network. Typically, as the training procedure evolves, the amount of improvement in the current model by a stochastic gradient update on each instance varies dynamically. In AutoAssist, we utilize this fact and design a simple instance shrinking operation, which is used to filter out instances with relatively low marginal improvement to the current model; thus the computationally intensive gradient computations are performed on informative instances as much as possible. We prove that the proposed technique outperforms vanilla SGD with existing importance sampling approaches for linear SVM problems, and establish an O(1/k) convergence for strongly convex problems. In order to apply the proposed techniques to accelerate training of deep models, we propose to jointly train a very lightweight Assistant network in addition to the original deep network referred to as Boss. The Assistant network is designed to gauge the importance of a given instance with respect to the current Boss such that a shrinking operation can be applied in the batch generator. With careful design, we train the Boss and Assistant in a nonblocking and asynchronous fashion such that overhead is minimal. We demonstrate that AutoAssist reduces the number of epochs by 40% for training a ResNet to reach the same test accuracy on an image classification data set and saves 30% training time needed for a transformer model to yield the same BLEU scores on a translation dataset.