Random-feature-based attention (RFA) is an efficient approximation of softmax attention with linear runtime and space complexity. However, the approximation gap between RFA and conventional softmax attention is not well studied. Built upon previous progress of RFA, we characterize this gap through the lens of control variates and show that RFA can be decomposed into a sum of multiple control variate estimators for each element in the sequence. This new framework reveals that exact softmax attention can be recovered from RFA by manipulating each control variate. Besides, it allows us to develop a more flexible form of control variates, resulting in a novel attention mechanism that significantly reduces the approximation gap while maintaining linear complexity. Extensive experiments demonstrate that our model outperforms state-of-the-art efficient attention mechanisms on both vision and language tasks.
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Idiap Research Institute（Idiap研究所）；Bielefeld University（比勒费尔德大学）
When data are organized in matrices or arrays of higher dimensions (tensors), classical regression methods first transform these data into vectors, therefore ignoring the underlying structure of the data and increasing the dimensionality of the problem. This flattening operation typically leads to overfitting when only few training data is available. In this paper, we present a mixture-of-experts model that exploits tensorial representations for regression of tensor-valued data. The proposed formulation takes into account the underlying structure of the data and remains efficient when few trai…
UniMamba: A Unified Spatial-Temporal Modeling Framework with State-Space and Attention Integration
School of Computing and Data Science, The University of Hong Kong, Hong Kong, China（计算与数据科学学院，香港大学，香港，中国）；School of Information Engineering, Beijing Institute of Graphic Communication, Beijing, China（信息工程学院，北京印刷学院，北京，中国）；Innovation Engineering College, Macau University of Science（创新工程学院，澳门科学技术大学）；Department of Computer Science and Technology, University of Cambridge, Cambridge, UK（计算机科学与技术系，剑桥大学，剑桥，英国）
University of Toronto（多伦多大学）；Stanford Cardiovascular Institute（斯坦福心血管研究所）
Deep learning provides an excellent avenue for optimizing diagnosis and patient monitoring for clinical-based applications, which can critically enhance the response time to the onset of various conditions. For cardiovascular disease, one such condition where the rising number of patients increasingly outweighs the availability of medical resources in different parts of the world, a core challenge is the automated classification of various cardiac abnormalities. Existing deep learning approaches have largely been limited to detecting the existence of an irregularity, as in binary classificatio…
Department of Computer Science, UIUC（伊利诺伊大学厄巴纳-香槟分校计算机科学系）；Department of Industrial and Enterprise Systems Engineering, UIUC（伊利诺伊大学厄巴纳-香槟分校工业与企业系统工程系）
The control variates (CV) method is widely used in policy gradient estimation to reduce the variance of the gradient estimators in practice. A control variate is applied by subtracting a baseline function from the state-action value estimates. Then the variance-reduced policy gradient presumably leads to higher learning efficiency. Recent research on control variates with deep neural net policies mainly focuses on scalar-valued baseline functions. The effect of vector-valued baselines is under-explored. This paper investigates variance reduction with coordinate-wise and layer-wise control vari…
College of Information and Computer Science（信息与计算机科学学院）；University of Massachusetts（马萨诸塞大学）；Amherst, MA 01003（阿默斯特，马萨诸塞州 01003）
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control variates. Despite the good results obtained, control variates developed for variational inference are typically looked at in isolation. In this paper we clarify the large number of control variates that are available by giving a systematic view of how they are derived. We also present…
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Southern Illinois University（南伊利诺伊大学）；University of Stuttgart（斯图加特大学）
In this work, we introduce a control variate approximation technique for low error approximate Deep Neural Network (DNN) accelerators. The control variate technique is used in Monte Carlo methods to achieve variance reduction. Our approach significantly decreases the induced error due to approximate multiplications in DNN inference, without requiring time-exhaustive retraining compared to state-of-the-art. Leveraging our control variate method, we use highly approximated multipliers to generate power-optimized DNN accelerators. Our experimental evaluation on six DNNs, for Cifar-10 and Cifar-10…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to exist…
DeepMind（深度思维）；Microsoft Research New England（微软新英格兰研究院）
Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach add…
National University of Singapore（新加坡国立大学）；IIT Bombay（印度理工学院孟买分校）
This paper studies a new variant of the stochastic multi-armed bandits problem where auxiliary information about the arm rewards is available in the form of control variates. In many applications like queuing and wireless networks, the arm rewards are functions of some exogenous variables. The mean values of these variables are known a priori from historical data and can be used as control variates. Leveraging the theory of control variates, we obtain mean estimates with smaller variance and tighter confidence bounds. We develop an upper confidence bound based algorithm named UCB-CV and charac…
Duke University（杜克大学）；Newcastle University（纽卡斯尔大学）；Imperial College London（伦敦帝国学院）；University College London（伦敦大学学院）
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial computational cost. This paper considers control variates based on Stein operators, presenting a framework that encompasses and generalizes existing approaches that use polynomials, kernels and neural networks. A learning strategy based on minimising a variational objective through stochastic optimization is proposed, leading to scalable and effective control var…
A key challenge for gradient based optimization methods in model-free reinforcement learning is to develop an approach that is sample efficient and has low variance. In this work, we apply Kronecker-factored curvature estimation technique (KFAC) to a recently proposed gradient estimator for control variate optimization, RELAX, to increase the sample efficiency of using this gradient estimation method in reinforcement learning. The performance of the proposed method is demonstrated on a synthetic problem and a set of three discrete control task Atari games.
Peking University（北京大学）；University of Lincoln（林肯大学）；Baidu Inc.（百度公司）；Beijing Institute of Big Data Research（北京大数据研究院）
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates approaches are well-known to reduce the variance of the estimation. These control variates are typically constructed by employing predefined parametric functions or polynomials, determined by using those samples drawn from the relevant distributions. Instead, we propose to construct those control variates by learning neural networks to handle the cases when tes…
Stochastic Multi-Armed Bandits with Limited Control Variates
Singapore-MIT Alliance for Research（新加坡-麻省理工联合研究与技术中心）；Technology Centre（技术中心）；Department of IEOR Indian Institute of Technology Bombay（工业工程与运营研究系印度理工学院班加罗尔）；Department of DSAI Indian Institute of Technology Madras（数据科学与人工智能系印度理工学院马德拉斯）
UESTC（电子科技大学）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Microsoft（微软）；Google（谷歌）；UIUC（伊利诺伊大学厄巴纳-香槟分校）
Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effectively reduce variance for policy gradient methods. Motivated by the Stein's identity, our method extends the previous control variate methods used in REINFORCE and advantage actor-critic by introducing more general action-dependent baseline functions. Empirical studies show tha…
We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand that is cheap to integrate. We show that a set of neural networks can face that challenge: a normalizing flow that approximates the shape of the integrand and another neural network that infers the solution of the integral equation. We also propose to leverage a neural importance sampler to estimate the difference between the original integrand and the learned …
Lancaster University（兰卡斯特大学）；University of Washington（华盛顿大学）
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despite this, there are a number of results suggesting that stochastic gradient Langevin dynamics (SGLD), probably the most popular of these methods, still has computational cost proportional to the dataset size. We suggest an alternative log posterior gradient estimate for stochastic…
Télécom Paris（巴黎电信学院）；Institut Polytechnique de Paris（巴黎理工学院）；CREST（经济与统计研究中心）；ENSAI（法国国立统计与信息分析学院）；UCLouvain（鲁汶天主教大学）
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of the particles to evolve during the algorithm, as is the case in sequential simulation methods. Within the standard adaptive importance sampling framework, a simple weighted least squares approach is proposed to improve the procedure with control variates. The procedure takes the form of a quadrature rule with adapted quadrature weights to reflect the informat…
Conditional neural control variates for variance reduction in Bayesian inverse problems
Department of Computer Science University of Central Florida（计算机科学系佛罗里达中央大学）；Department of Physics and Maryland Center for Fundamental Physics University of Maryland College Park（物理系马里兰根本物理中心马里兰大学学院公园分校）
While many areas of machine learning have benefited from the increasing availability of large and varied datasets, the benefit to causal inference has been limited given the strong assumptions needed to ensure identifiability of causal effects; these are often not satisfied in real-world datasets. For example, many large observational datasets (e.g., case-control studies in epidemiology, click-through data in recommender systems) suffer from selection bias on the outcome, which makes the average treatment effect (ATE) unidentifiable. We propose a general algorithm to estimate causal effects fr…
Multi-step temporal difference (TD) learning is an important approach in reinforcement learning, as it unifies one-step TD learning with Monte Carlo methods in a way where intermediate algorithms can outperform either extreme. They address a bias-variance trade off between reliance on current estimates, which could be poor, and incorporating longer sampled reward sequences into the updates. Especially in the off-policy setting, where the agent aims to learn about a policy different from the one generating its behaviour, the variance in the updates can cause learning to diverge as the number of…
We study the problem of off-policy evaluation from batched contextual bandit data with multidimensional actions, often termed slates. The problem is common to recommender systems and user-interface optimization, and it is particularly challenging because of the combinatorially-sized action space. Swaminathan et al. (2017) have proposed the pseudoinverse (PI) estimator under the assumption that the conditional mean rewards are additive in actions. Using control variates, we consider a large class of unbiased estimators that includes as specific cases the PI estimator and (asymptotically) its se…
Columbia University（哥伦比亚大学）；Google Robotics（谷歌机器人）；Fero Labs（费罗实验室）
Evolution Strategies (ES) are a powerful class of blackbox optimization techniques that recently became a competitive alternative to state-of-the-art policy gradient (PG) algorithms for reinforcement learning (RL). We propose a new method for improving accuracy of the ES algorithms, that as opposed to recent approaches utilizing only Monte Carlo structure of the gradient estimator, takes advantage of the underlying MDP structure to reduce the variance. We observe that the gradient estimator of the ES objective can be alternatively computed using reparametrization and PG estimators, which leads…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Gradient-based optimization is the foundation of deep learning and reinforcement learning. Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still often the best strategy. We introduce a general framework for learning low-variance, unbiased gradient estimators for black-box functions of random variables. Our method uses gradients of a neural network trained jointly with model parameters or policies, and is applicable in both discrete and continuous settings. We demonstrate this framework for training discr…
Neural Autoregressive Control Variates for the Quantum Monte Carlo Sign Problem
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China（北京凝聚态物理国家实验室和物理研究所，中国科学院，北京100190，中国）；University of Chinese Academy of Sciences, Beijing 100049, China（中国科学院大学，北京100049，中国）
Control Variate Score Matching for Diffusion Models
Google DeepMind（谷歌DeepMind）；BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究院）；Machine Learning Group, Technische Universität Berlin（柏林技术大学机器学习组）；Department of Artificial Intelligence, Korea University（韩国大学人工智能系）；Max-Planck Institute for Informatics（马克斯·普朗克信息研究所）
In many computational science and engineering applications, the output of a system of interest corresponding to a given input can be queried at different levels of fidelity with different costs. Typically, low-fidelity data is cheap and abundant, while high-fidelity data is expensive and scarce. In this work we study the reinforcement learning (RL) problem in the presence of multiple environments with different levels of fidelity for a given control task. We focus on improving the RL agent's performance with multifidelity data. Specifically, a multifidelity estimator that exploits the cross-co…
Off-policy learning is powerful for reinforcement learning. However, the high variance of off-policy evaluation is a critical challenge, which causes off-policy learning falls into an uncontrolled instability. In this paper, for reducing the variance, we introduce control variate technique to $\mathtt{Expected}$ $\mathtt{Sarsa}$($λ$) and propose a tabular $\mathtt{ES}$($λ$)-$\mathtt{CV}$ algorithm. We prove that if a proper estimator of value function reaches, the proposed $\mathtt{ES}$($λ$)-$\mathtt{CV}$ enjoys a lower variance than $\mathtt{Expected}$ $\mathtt{Sarsa}$($λ$). Furthermore, to e…
Policy gradient methods have demonstrated success in reinforcement learning tasks that have high-dimensional continuous state and action spaces. However, policy gradient methods are also notoriously sample inefficient. This can be attributed, at least in part, to the high variance in estimating the gradient of the task objective with Monte Carlo methods. Previous research has endeavored to contend with this problem by studying control variates (CVs) that can reduce the variance of estimates without introducing bias, including the early use of baselines, state dependent CVs, and the more recent…
College of Information and Computer Science（信息与计算机科学学院）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme by minimizing the gradient estimator's variance. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with n…
