We propose a novel strategy for Neural Architecture Search (NAS) based on Bregman iterations. Starting from a sparse neural network our gradient-based one-shot algorithm gradually adds relevant parameters in an inverse scale space manner. This allows the network to choose the best architecture in the search space which makes it well-designed for a given task, e.g., by adding neurons or skip connections. We demonstrate that using our approach one can unveil, for instance, residual autoencoders for denoising, deblurring, and classification tasks. Code is available at https://github.com/TimRoith/BregmanLearning.
In the paper, we design a novel Bregman gradient policy optimization framework for reinforcement learning based on Bregman divergences and momentum techniques. Specifically, we propose a Bregman gradient policy optimization (BGPO) algorithm based on the basic momentum technique and mirror descent iteration. Meanwhile, we further propose an accelerated Bregman gradient policy optimization (VR-BGPO) algorithm based on the variance reduced technique. Moreover, we provide a convergence analysis framework for our Bregman gradient policy optimization under the nonconvex setting. We prove that our BG…
University of California, Irvine（加利福尼亚大学欧文分校）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to solve the regularized maximum likelihood estimation problem. We show that our method is significantly faster than the widely used graphical lasso method, which is based on blockwise coordinate descent, on both artificial and real-world data. More importantly, different from the graphical lasso, the split Bregman based method is much more general, and can be…
Iowa State University（爱荷华州立大学）；IBM Research AI（IBM人工智能研究院）
We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global Lipschitz-continuous (partial) gradient assumption. Under the notion of relative smoothness based on the Bregman distance, we prove that every limit point of the generated sequence is a stationary point. Further, we show that the iteration complexity of the proposed method is $O(n\varepsilon^{-2})$ to achieve $ε$-stationary point, where $n$ is the number of blocks…
Howard Hughes Medical Institute, Janelia Farm Research Campus（霍华德·休斯医学研究所，贾尼利亚农场研究园区）
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and der…
Fudan University（复旦大学）；Peking University（北京大学）；Hong Kong University of Science and Technology（香港科技大学）
This paper proposes a novel Stochastic Split Linearized Bregman Iteration ($S^{2}$-LBI) algorithm to efficiently train the deep network. The $S^{2}$-LBI introduces an iterative regularization path with structural sparsity. Our $S^{2}$-LBI combines the computational efficiency of the LBI, and model selection consistency in learning the structural sparsity. The computed solution path intrinsically enables us to enlarge or simplify a network, which theoretically, is benefited from the dynamics property of our $S^{2}$-LBI algorithm. The experimental results validate our $S^{2}$-LBI on MNIST and CI…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard $\ell_1$ regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-f…
Paradigm Inc（第四范式公司）；Center for Data Science, Peking University（北京大学数据科学中心）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Beijing Institute of Big Data Research (BIBDR)（北京大数据研究院）
Neural architecture search (NAS) recently attracts much research attention because of its ability to identify better architectures than handcrafted ones. However, many NAS methods, which optimize the search process in a discrete search space, need many GPU days for convergence. Recently, DARTS, which constructs a differentiable search space and then optimizes it by gradient descent, can obtain high-performance architecture and reduces the search time to several days. However, DARTS is still slow as it updates an ensemble of all operations and keeps only one after convergence. Besides, DARTS ca…
Hausdorff Center for Mathematics（豪斯多夫数学中心）；University of Bonn（波恩大学）；Friedrich–Alexander University Erlangen–Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We derive a baseline algorithm called LinBreg, an accelerated version using momentum, and AdaBreg, which is a Bregmanized generalization of the Adam algorithm. In contrast to established methods for sparse training the proposed family of algorithms constitutes a regrowth strategy for neural networks that is solely optimization-based without additional heuristics. Our Bregman learning framework starts the training with very f…
Technical University of Munich（慕尼黑工业大学）；Saarland University（萨尔兰大学）
A typical assumption for the analysis of first order optimization methods is the Lipschitz continuity of the gradient of the objective function. However, for many practical applications this assumption is violated, including loss functions in deep learning. To overcome this issue, certain extensions based on generalized proximity measures known as Bregman distances were introduced. This initiated the development of the Bregman proximal gradient (BPG) algorithm and an inertial variant (momentum based) CoCaIn BPG, which however rely on problem dependent Bregman distances. In this paper, we devel…
Purdue University（普渡大学）；University of Chicago（芝加哥大学）
Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (\mcn) is an effective approach. All state-of-the-art algorithms for optimizing \mcn\ objectives take at least $O(1/ε)$ number of iterations to find an $ε$ accurate solution. Recent results in structured optimization suggest that faster rates are possible by exploiting the structure of the objective function. Towards this end \citet{Nesterov05} proposed an excessive gap reduction technique based on Euclidean projections which converges in $O(1/\sqrtε)$ iterations…
This paper studies approximate policy iteration (API) methods which use least-squares Bellman error minimization for policy evaluation. We address several of its enhancements, namely, Bellman error minimization using instrumental variables, least-squares projected Bellman error minimization, and projected Bellman error minimization using instrumental variables. We prove that for a general discrete-time stochastic control problem, Bellman error minimization using instrumental variables is equivalent to both variants of projected Bellman error minimization. An alternative to these API methods is…
Making a simple model by choosing a limited number of features with the purpose of reducing the computational complexity of the algorithms involved in classification is one of the main issues in machine learning and data mining. The aim of Feature Selection (FS) is to reduce the number of redundant and irrelevant features and improve the accuracy of classification in a data set. We propose an efficient ISPSO-GLOBAL (Improved Seeding Particle Swarm Optimization GLOBAL) method which investigates the specified iterations to produce prominent features and store them in storage list. The goal is to…
DeepMind（深度思考）；OpenAI；University of California, Berkeley（加州大学伯克利分校）；Google Brain（谷歌大脑）
Monte Carlo Tree Search (MCTS) algorithms perform simulation-based search to improve policies online. During search, the simulation policy is adapted to explore the most promising lines of play. MCTS has been used by state-of-the-art programs for many problems, however a disadvantage to MCTS is that it estimates the values of states with Monte Carlo averages, stored in a search tree; this does not scale to games with very high branching factors. We propose an alternative simulation-based search method, Policy Gradient Search (PGS), which adapts a neural network simulation policy online via pol…
Hyperparameter tuning is a common technique for improving the performance of neural networks. Most techniques for hyperparameter search involve an iterated process where the model is retrained at every iteration. However, the expected accuracy improvement from every additional search iteration, is still unknown. Calculating the expected improvement can help create stopping rules for hyperparameter tuning and allow for a wiser allocation of a project's computational budget. In this paper, we establish an empirical estimate for the expected accuracy improvement from an additional iteration of hy…
The combination of Monte-Carlo Tree Search (MCTS) and deep reinforcement learning is state-of-the-art in two-player perfect-information games. In this paper, we describe a search algorithm that uses a variant of MCTS which we enhanced by 1) a novel action value normalization mechanism for games with potentially unbounded rewards (which is the case in many optimization problems), 2) defining a virtual loss function that enables effective search parallelization, and 3) a policy network, trained by generations of self-play, to guide the search. We gauge the effectiveness of our method in "SameGam…
Solving optimal design problems through crowdsourcing faces a dilemma: On one hand, human beings have been shown to be more effective than algorithms at searching for good solutions of certain real-world problems with high-dimensional or discrete solution spaces; on the other hand, the cost of setting up crowdsourcing environments, the uncertainty in the crowd's domain-specific competence, and the lack of commitment of the crowd, all contribute to the lack of real-world application of design crowdsourcing. We are thus motivated to investigate a solution-searching mechanism where an optimizatio…
Coordinate descent is one of the most popular approaches for solving Lasso and its extensions due to its simplicity and efficiency. When applying coordinate descent to solving Lasso, we update one coordinate at a time while fixing the remaining coordinates. Such an update, which is usually easy to compute, greedily decreases the objective function value. In this paper, we aim to improve its computational efficiency by reducing the number of coordinate descent iterations. To this end, we propose a novel technique called Successive Ray Refinement (SRR). SRR makes use of the following ray continu…
Expert Iteration (ExIt) is an effective framework for learning game-playing policies from self-play. ExIt involves training a policy to mimic the search behaviour of a tree search algorithm - such as Monte-Carlo tree search - and using the trained policy to guide it. The policy and the tree search can then iteratively improve each other, through experience gathered in self-play between instances of the guided tree search algorithm. This paper outlines three different approaches for manipulating the distribution of data collected from self-play, and the procedure that samples batches for learni…
We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI) scheme via an -approximate greedy operator (Kakade and Langford, 2002; Lazaric et al., 2010). We describe existing and a few new performance bounds for Direct Policy Iteration (DPI) (Lagoudakis and Parr, 2003; Fern et al., 2006; Lazaric et al., 2010) and Conservative Policy Iteration (CPI) (Kakade and Langford, 2002). By paying a particular attention to the …
We present an algorithm for local, regularized, policy improvement in reinforcement learning (RL) that allows us to formulate model-based and model-free variants in a single framework. Our algorithm can be interpreted as a natural extension of work on KL-regularized RL and introduces a form of tree search for continuous action spaces. We demonstrate that additional computation spent on model-based policy improvement during learning can improve data efficiency, and confirm that model-based policy improvement during action selection can also be beneficial. Quantitatively, our algorithm improves …
