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Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform averages of the iterates converge at a O(1/T) rate in terms of the saddle-point residual. However, numerically, the iterates themselves can often converge much faster than the uniform averages. This observation motivates increasing averaging schemes that put more weight on later iterates, in contrast to the usual uniform averaging. We show that such increasing averaging schemes, applied to various first-order methods, are able to preserve the O(1/T) convergence rate with no additional assumptions or computational overhead. Extensive numerical experiments on zero-sum game solving, market equilibrium computation and image denoising demonstrate the effectiveness of the proposed schemes. In particular, the increasing averages consistently outperform the uniform averages in all test problems by orders of magnitude. When solving matrix and extensive-form games, increasing averages consistently outperform the last iterates as well. For matrix games, a first-order method equipped with increasing averaging outperforms the highly competitive CFR+ algorithm.

AAAI 2021

Increasing Iterate Averaging for Solving Saddle-Point Problems

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through the example of the classical NP-hard Knapsack Problem. Our main contribution is a class of recurrent neural networks (RNNs) with rectified linear units that are iteratively applied to each item of a Knapsack instance and thereby compute optimal or provably good solution values. We show that an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient to find optimum Knapsack solutions. We also prove the following tradeoff between the size of an RNN and the quality of the computed Knapsack solution: for Knapsack instances consisting of n items, an RNN of depth five and width w computes a solution of value at least 1 - O(n^2 sqrt(w)) times the optimum solution value. Our results build upon a classical dynamic programming formulation of the Knapsack Problem as well as a careful rounding of profit values that are also at the core of the well-known fully polynomial-time approximation scheme for the Knapsack Problem. Finally, we point out that our results can be generalized to many other combinatorial optimization problems that admit dynamic programming solution methods, such as various Shortest Path Problems, the Longest Common Subsequence Problem, and the Traveling Salesperson Problem.

Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size

Federated learning enables clients to collaboratively learn a shared global model without sharing their local training data with a cloud server. However, malicious clients can corrupt the  global  model  to  predict  incorrect  labels  for  testing  examples. Existing defenses against malicious clients leverage Byzantine-robust federated learning methods. However, these methods cannot provably guarantee that the predicted label for  a  testing  example  is  not  affected  by  malicious  clients. We bridge this gap via ensemble federated learning. In particular, given any base federated learning algorithm, we use the algorithm to learn multiple global models, each of which is learnt using a randomly selected subset of clients. When predicting  the  label  of  a  testing  example,  we  take  majority vote  among  the  global  models.  We  show  that  our  ensemble  federated  learning  with  any  base  federated  learning  algorithm is provably secure against malicious clients. Specifically, the label predicted by our ensemble global model for a testing example is provably not affected by a bounded number of malicious clients. Moreover, we show that our derived bound is tight. We evaluate our method on MNIST and Human Activity Recognition datasets. For instance, our method can achieve a certified accuracy of 88% on MNIST when 20 out of 1,000 clients are malicious.

Provably Secure Federated Learning against Malicious Clients

Safe exploration is regarded as a key priority area for reinforcement learning research.
With separate reward and safety signals, it is natural to cast it as constrained reinforcement learning, where expected long-term costs of policies are constrained.
However, it can be hazardous to set constraints on the expected safety signal without considering the tail of the distribution.
For instance, in safety-critical domains, worst-case analysis is required to avoid disastrous results.
We present a novel reinforcement learning algorithm called Worst-Case Soft Actor Critic, which extends the Soft Actor Critic algorithm with a safety critic to achieve risk control.
More specifically, a certain level of conditional Value-at-Risk from the distribution is regarded as a safety measure to judge the constraint satisfaction, which guides the change of adaptive safety weights to achieve a trade-off between reward and safety.
As a result, we can optimize policies under the premise that their worst-case performance satisfies the constraints. The empirical analysis shows that our algorithm attains better risk control compared to expectation-based methods.

WCSAC: Worst-Case Soft Actor Critic for Safety-Constrained Reinforcement Learning

Existing global convergence guarantees of (stochastic) gradient descent do not apply to practical deep networks in the practical regime of deep learning beyond the neural tangent kernel (NTK) regime. This paper proposes an algorithm, which is ensured to have global convergence guarantees in the practical regime beyond the NTK regime, under a verifiable condition called the expressivity condition. The expressivity condition is defined to be both data-dependent and architecture-dependent, which is the key property that makes our results applicable for practical settings beyond the NTK regime. On the one hand, the expressivity condition is theoretically proven to hold data-independently for fully-connected deep neural networks with narrow hidden layers and a single wide layer. On the other hand, the expressivity condition is numerically shown to hold data-dependently for deep (convolutional) ResNet with batch normalization with various standard image datasets. We also show that the the proposed algorithm has generalization performances comparable with those of the heuristic algorithm, with the same hyper-parameters and total number of iterations. Therefore, the proposed algorithm can be viewed as a step towards providing theoretical guarantees for deep learning in the practical regime.

A Recipe for Global Convergence Guarantee in Deep Neural Networks

When can we expect a text-video retrieval system to work effectively on datasets that differ from its training domain?  In this work, we investigate this question through the lens of unsupervised domain adaptation in which the objective is to match natural language queries and video content in the presence of domain shift at query-time.  Such systems have significant practical applications since they are capable generalising to new data sources without requiring corresponding text annotations. We make the following contributions: (1) We propose the  UDAVR (Unsupervised Domain Adaptation for Video Retrieval) benchmark and employ it to study the performance of text-video retrieval in the presence of domain
shift. (2) We propose Concept-Aware-Pseudo-Query (CAPQ), a method for learning discriminative and transferable features that bridge these cross-domain discrepancies to enable effective target domain retrieval using source domain supervision. (3) We show that CAPQ outperforms alternative domain adaptation strategies on UDAVR.

Mind-the-Gap! Unsupervised Domain Adaptation for Text-Video Retrieval

In finance, the momentum spillovers of listed firms is well acknowledged. Only few studies predicted the trend of one firm in terms of its relevant firms. A common strategy of the pilot work is to adopt graph convolution networks (GCNs) with some predefined firm relations. However, momentum spillovers are propagated via a variety of firm relations, of which the bridging importance varies with time. Restricting to several predefined relations inevitably makes noise and thus misleads stock predictions. In addition, traditional GCNs transfer and aggregate the peer influences without considering the states of both connected firms once a connection is built. Such non-attribute sensibility makes traditional GCNs inappropriate to deal with the attribute-sensitive momentum spillovers of listed firms wherein the abnormal price drop of one firm may not spill over if the trade volume of this decreasing price is small or the prices of the linked firms are undervalued. In this study, we propose an attribute-driven graph attention network (AD-GAT) to address both problems in modeling momentum spillovers. This is achieved by element-wisely multiplying the nonlinear transformation of the attributes of the connected firms with the attributes of the source firm to consider its attribute-sensitive momentum spillovers, and applying the unmasked attention mechanism to infer the general dynamic firm relation from observed market signals fused by a novel tensor-based feature extractor. Experiments on the three-year data of the S&P 500 demonstrate the superiority of the proposed framework over stateof-the-art algorithms, including GCN, eLSTM, and TGC.

Modeling the Momentum Spillover Effect for Stock Prediction via Attribute-Driven Graph Attention Networks

End-to-end delay is a critical attribute of quality of service (QoS) in application domains such as cloud computing and computer networks. This metric is particularly important in tandem service systems, where the end-to-end service is provided through a chain of services. Service-rate control is a common mechanism for providing QoS guarantees in service systems. In this paper, we introduce a reinforcement learning-based (RL-based) service-rate controller that provides probabilistic upper-bounds on the end-to-end delay of the system, while preventing the overuse of service resources. In order to have a general framework, we use queueing theory to model the service systems. However, we adopt an RL-based approach to avoid the limitations of queueing-theoretic methods. In particular, we use Deep Deterministic Policy Gradient (DDPG) to learn the service rates (action) as a function of the queue lengths (state) in tandem service systems. In contrast to existing RL-based methods that quantify their performance by the achieved overall reward, which could be hard to interpret or even misleading, our proposed controller provides explicit probabilistic guarantees on the end-to-end delay of the system. The evaluations are presented for a tandem queueing system with non-exponential inter-arrival and service times, the results of which validate our controller's capability in meeting QoS constraints.

Queue-Learning: A Reinforcement Learning Approach for Providing Quality of Service

Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide not only accurate prediction but also attractive interpretability through search-based methods. However, existing methods suffer from slow kernel composition learning. To tackle large-scaled data, we propose a new sparse approximate posterior for GPs, MultiSVGP, constructed from groups of inducing points associated with individual additive kernels in compositional kernels. We demonstrate that this approximation provides a better fit to learn compositional kernels given empirical observations. We also provide theoretically justification on error bound when compared to the traditional sparse GP. In contrast to the search-based approach, we present a novel probabilistic algorithm to learn a kernel composition by handling the sparsity in the kernel selection with Horseshoe prior. We demonstrate that our model can capture characteristics of time series with significant reductions in computational time and have competitive regression performance on real-world data sets.

Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior

Depth estimation in real-world applications requires precise responses to fast motion and challenging lighting conditions. Event cameras use bio-inspired event-driven sensors that provide instantaneous and asynchronous information of pixel-level log intensity changes, which makes them suitable for depth estimation in such challenging conditions. However, as the event cameras primarily provide asynchronous and spatially sparse event data, it is hard to provide accurate dense disparity map in stereo event camera setups - especially in estimating disparities on local structures or edges. In this study, we develop a novel deep event stereo network that reconstructs spatial intensity image features from embedded event streams and leverages the event features using the reconstructed image features to compute dense disparity maps. To this end, we propose a novel event-to-image translation network with a cross-semantic attention mechanism that calculates the global semantic context of the event features for the intensity image reconstruction. In addition, a feature aggregation module is developed for accurate disparity estimation, which modulates the event features with the reconstructed image features by a stacked dilated spatially-adaptive denormalization mechanism. Experimental results reveal that our method can outperform the state-of-the-art methods by significant margins both in quantitative and qualitative measures.

Deep Event Stereo Leveraged by Event-to-Image Translation

Aspect based sentiment analysis (ABSA) involves three fundamental subtasks: aspect term extraction, opinion term extraction, and aspect-level sentiment classification. Early works only focused on solving one of these subtasks individually. Some recent work focused on solving a combination of two subtasks, e.g., extracting aspect terms along with sentiment polarities or extracting the aspect and opinion terms pair-wisely. More recently, the triple extraction task has been proposed, i.e., extracting the (aspect term, opinion term, sentiment polarity) triples from a sentence. However, previous approaches fail to solve all subtasks in a unified end-to-end framework. In this paper, we propose a complete solution for ABSA. We construct two machine reading comprehension (MRC) problems, and solve all subtasks by joint training two BERT-MRC models with parameters sharing. We conduct experiments on these subtasks and results on several benchmark datasets demonstrate the effectiveness of our proposed framework, which significantly outperforms existing state-of-the-art methods.

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