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Decentralized stochastic gradient descent methods have attracted increasing interest in recent years. Numerous methods have been proposed for the nonconvex finite-sum optimization problem.  However, existing methods have a large sample complexity,  slowing down the empirical convergence speed. To address this issue, in this paper, we proposed a novel decentralized stochastic gradient descent method for the nonconvex finite-sum optimization problem, which enjoys a better sample and communication complexity than existing methods. To the best of our knowledge, our work is the first one achieving such favorable sample and communication complexities. Finally, we have conducted extensive experiments and the experimental results have confirmed the superior performance of our proposed method.

AAAI 2022

Efficient Decentralized Stochastic Gradient Descent Method for Nonconvex Finite-Sum Optimization 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. 

AAAI 2021

technical paper

Learning effective embeddings for potentially irregularly sampled time-series, evolving at different time scales, is fundamental for machine learning tasks such as classification and clustering. Task-dependent embeddings rely on similarities between data samples to learn effective geometries. However, many popular time-series similarity measures are not valid distance metrics, and as a result they do not reliably capture the intricate relationships between the multi-variate time-series data samples for learning effective embeddings. One of the primary ways to formulate an accurate distance metric is by forming distance estimates via Monte-Carlo-based expectation evaluations. However, the high-dimensionality of the underlying distribution, and the inability to sample from it, pose significant challenges. To this end, we develop an Importance Sampling based distance metric -- I-SEA -- which enjoys the properties of a metric while consistently achieving superior performance for machine learning tasks such as classification and representation learning. I-SEA leverages Importance Sampling and Non-parametric Density Estimation to adaptively estimate distances, enabling implicit estimation from the underlying high-dimensional distribution, resulting in improved accuracy and reduced variance. We theoretically establish the properties of I-SEA and demonstrate its capabilities via experimental evaluations on real-world healthcare datasets.

I-SEA: Importance Sampling and Expected Alignment-Based Deep Distance Metric Learning for Time Series Analysis and Embedding

Due to the surge of cloud-assisted AI services, the problem of designing resilient prediction serving systems that can effectively cope with stragglers and minimize response delays has attracted much interest. The common approach for tackling this problem is replication which assigns the same prediction task to multiple workers. This approach, however, is  inefficient and incurs significant resource overheads. Hence, a learning-based approach known as parity model (ParM) has been recently proposed which learns models that can generate ``parities'' for a group of predictions  to reconstruct the predictions of the slow/failed workers. While this learning-based approach is more resource-efficient than replication, it is tailored to the specific model hosted by the cloud and is particularly suitable for a small number of queries (typically less than four) and tolerating very few stragglers (mostly one). Moreover, ParM does not handle Byzantine adversarial workers. We propose a different approach, named Approximate Coded Inference (ApproxIFER), that does not require training any parity models, hence it is agnostic to the model hosted by the cloud and can be readily applied to different data domains and model architectures. Compared with earlier works, ApproxIFER can handle a general number of stragglers and scales significantly better with the  number of queries. Furthermore, ApproxIFER is robust against Byzantine workers. Our extensive experiments on a large number of datasets and model architectures show significant degraded mode accuracy improvement by up to 58% over ParM.

ApproxIFER: A Model-Agnostic Approach to Resilient and Robust Prediction Serving Systems

The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity, model parameters with high likelihood might not necessarily result in high performance of the agent on a downstream control task. To alleviate this problem, we propose an end-to-end approach for model learning which directly optimizes the expected returns using implicit differentiation. We treat a value function that satisfies the Bellman optimality operator induced by the model as an implicit function of model parameters and show how to differentiate the function. We provide theoretical and empirical evidence highlighting the benefits of our approach in the model misspecification regime compared to likelihood-based methods.

Control-Oriented Model-Based Reinforcement Learning with Implicit Differentiation

The efficient detection of outbreaks and other cascading phenomena is a fundamental problem in a number of domains, including disease spread, social networks, and infrastructure networks. In such settings, monitoring and testing a small group of pre-selected nodes from the susceptible population (i.e., a sensor set) is often the preferred testing regime. We study the problem of selecting a sensor set that minimizes the delay in detection---we refer to this as the MinDelSS problem. Prior methods for minimizing the detection time rely on greedy algorithms using submodularity. We show that this approach can sometimes lead to a worse approximation for minimizing the detection time than desired. We also show that MinDelSS is hard to approximate within an O(n^(1-1/g))-factor for any constant g greater than or equal to 2 for a graph with n nodes. This instead motivates seeking a bicriteria approximations. We present the algorithm RoundSensor, which gives a rigorous worst case O(log(n))-factor for the detection time, while violating the budget by a factor of O(log^2(n)). Our algorithm is based on the sample average approximation technique from stochastic optimization, combined with linear programming and rounding. We evaluate our algorithm on several networks, including hospital contact networks, which validates its effectiveness in real settings.

Provable Sensor Sets for Epidemic Detection over Networks with Minimum Delay

Co-training, extended from self-training, is one of the frameworks for semi-supervised learning. Without natural split of features, single-view co-training works at the cost of training extra classifiers, where the algorithm should be delicately designed to prevent individual classifiers from collapsing into each other. To remove these obstacles which deter the adoption of single-view co-training, we present a simple and efficient algorithm Multi-Head Co-Training. By integrating base learners into a multi-head structure, the model is in a minimal amount of extra parameters. Every classification head in the unified model interacts with its peers through a â€œWeak and Strong Augmentationâ€ strategy, in which the diversity is naturally brought by the strong data augmentation. Therefore, the proposed method facilitates single-view co-training by 1). promoting diversity implicitly and 2). only requiring a small extra computational overhead. The effectiveness of Multi-Head Co-Training is demonstrated in an empirical study on standard semi-supervised learning benchmarks.

Semi-Supervised Learning with Multi-Head Co-Training

Model-based reinforcement learning algorithms, which aim to learn a model of the environment to make decisions, are more sample efficient than their model-free counterparts. The sample efficiency of model-based approaches relies on whether the model can well approximate the environment. However, learning an accurate model is challenging, especially in complex and noisy environments. To tackle this problem, we propose the conservative model-based actor-critic (CMBAC), a novel approach that achieves high sample efficiency without the strong reliance on accurate learned models. Specifically, CMBAC learns multiple estimates of the Q-value function from a set of inaccurate models and uses the average of the bottom-k estimates---a conservative estimate---to optimize the policy. An appealing feature of CMBAC is that the conservative estimates effectively encourage the agent to avoid unreliable â€œpromising actionsâ€---whose values are high in only a small fraction of the models. Experiments demonstrate that CMBAC significantly outperforms state-of-the-art approaches in terms of sample efficiency on several challenging control tasks, and the proposed method is more robust than previous methods in noisy environments.

Sample-Efficient Reinforcement Learning via Conservative Model-Based Actor-Critic

Knowledge Graph Question Answering (KGQA) involves retrieving facts from a Knowledge Graph (KG) using natural language queries. A KG is a curated set of facts consisting of entities linked by relations. Certain facts include also temporal information forming a Temporal KG (TKG). Although many natural questions involve explicit or implicit time constraints, question answering (QA) over TKGs has been a relatively unexplored area. Existing solutions are mainly designed for simple temporal questions that can be answered directly by a single TKG fact.
 This paper puts forth a comprehensive embedding-based framework for answering complex questions over TKGs. Our method termed temporal question reasoning (TempoQR) exploits TKG embeddings to ground the question to the specific entities and time scope it refers to. It does so by augmenting the question embeddings with context, entity and time-aware information by employing three specialized modules. The first computes a textual representation of a given question, the second combines it with the entity embeddings for entities involved in the question, and the third generates question-specific time embeddings. Finally, a transformer-based encoder learns to fuse the generated temporal information with the question representation, which is used for answer predictions. Extensive experiments show that TempoQR improves accuracy by 25--45 percentage points on complex temporal questions over state-of-the-art approaches and it generalizes better to unseen question types.

TempoQR: Temporal Question Reasoning over Knowledge Graphs

Multimodal sensors (visual, non-visual, and wearable) can provide complementary information to develop robust perception systems for recognizing activities accurately. However, it is challenging to extract robust multimodal representations due to the heterogeneous characteristics of data from multimodal sensors and disparate human activities, especially in the presence of noisy and misaligned sensor data. In this work, we propose a cooperative multitask learning-based guided multimodal fusion approach, MuMu, to extract robust multimodal representations for human activity recognition (HAR). MuMu employs an auxiliary task learning approach to extract features specific to each set of activities with shared characteristics (activity-group). MuMu then utilizes activity-group-specific features to direct our proposed Guided Multimodal Fusion Approach (GM-Fusion) for extracting complementary multimodal representations, designed as the target task. We evaluated MuMu by comparing its performance to state-of-the-art multimodal HAR approaches on three activity datasets. Our extensive experimental results suggest that MuMu outperforms all the evaluated approaches across all three datasets. Additionally, the ablation study suggests that MuMu significantly outperforms the baseline models (p<0.05), which do not use our guided multimodal fusion. Finally, the robust performance of MuMu on noisy and misaligned sensor data posits that our approach is suitable for HAR in real-world settings.

MuMu: Cooperative Multitask Learning-Based Guided Multimodal Fusion

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invarianceâ€”the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Pushing the Limits of Rule Reasoning in Transformers through Natural Language Satisfiability

Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not known to hold generally with dependent samples, such as in online learning with time series data or distributed computing with Markovian training samples. In this paper, we show that SAA remains tractable when the distribution of unknown parameters is only observable through dependent instances and still enjoys asymptotic consistency and finite sample guarantees. Specifically, we provide a rigorous probability error analysis to derive 1 - beta confidence bounds for the out-of-sample performance of SAA estimators and show that these estimators are asymptotically consistent. We then, using monotone operator theory, study the performance of a class of stochastic first-order algorithms trained on a dependent source of data. We show that approximation error for these algorithms is bounded and concentrates around zero, and establish deviation bounds for iterates when the underlying stochastic process is phi-mixing. The algorithms presented can be used to handle numerically inconvenient loss functions such as the sum of a smooth and non-smooth function or of non-smooth functions with constraints. To illustrate the usefulness of our results, we present several stochastic versions of popular algorithms such as stochastic proximal gradient descent (S-PGD), stochastic relaxed Peaceman-Rachford splitting algorithms (S-rPRS), and numerical experiment.

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