A BSTRACT Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space. These difficulties can be addressed by second-order approaches that apply a preconditioning matrix to the gradient to improve convergence. Unfortunately, such algorithms typically struggle to scale to high-dimensional problems, in part because the calculation of specific preconditioners such as the inverse Hessian or Fisher information matrix is highly expensive. We introduce first-order preconditioning (FOP), a fast, scalable approach that generalizes previous work on hyper-gradient descent (Almeida et al., 1998; Maclaurin et al., 2015; Baydin et al., 2017) to learn a preconditioning matrix that only makes use of first-order information. Experiments show that FOP is able to improve the performance of standard deep learning optimizers on several visual classification tasks with minimal computational overhead. We also investigate the properties of the learned preconditioning matrices and perform a preliminary theoretical analysis of the algorithm. Despite this, deep neural networks and other large-scale machine learning models applied to such problems typically rely on simple variations of gradient descent to train, which is known to be highly sensitive to these difficulties.

We consider a setting in which the objective is to learn to navigate in a controlled Markov process (CMP) where transition probabilities may abruptly change. For this setting, we propose a performance measure called exploration steps which counts the time steps at which the learner lacks sufficient knowledge to navigate its environment efficiently. We devise a learning meta-algorithm, MNM, and prove an upper bound on the exploration steps in terms of the number of changes.

Reinforcement learning, mathematically described by Markov Decision Problems, may be approached either through dynamic programming or policy search. Actor-critic algorithms combine the merits of both approaches by alternating between steps to estimate the value function and policy gradient updates. Due to the fact that the updates exhibit correlated noise and biased gradient updates, only the asymptotic behavior of actor-critic is known by connecting its behavior to dynamical systems. This work puts forth a new variant of actor-critic that employs Monte Carlo rollouts during the policy search updates, which results in controllable bias that depends on the number of critic evaluations. As a result, we are able to provide for the first time the convergence rate of actor-critic algorithms when the policy search step employs policy gradient, agnostic to the choice of policy evaluation technique. In particular, we establish conditions under which the sample complexity is comparable to stochastic gradient method for non-convex problems or slower as a result of the critic estimation error, which is the main complexity bottleneck. These results hold for in continuous state and action spaces with linear function approximation for the value function. We then specialize these conceptual results to the case where the critic is estimated by Temporal Difference, Gradient Temporal Difference, and Accelerated Gradient Temporal Difference. These learning rates are then corroborated on a navigation problem involving an obstacle, which suggests that learning more slowly may lead to improved limit points, providing insight into the interplay between optimization and generalization in reinforcement learning.

In engineering applications almost all processes are described with the aid of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller's performance. In this paper we propose an approach to identify model uncertainty using parameter identification and optimal design of experiments. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions, in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data or parameter uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.

Space-filling designs such as scrambled-Hammersley, Latin Hypercube Sampling and Jittered Sampling have been proposed for fully parallel hyperparameter search, and were shown to be more effective than random or grid search. In this paper, we show that these designs only improve over random search by a constant factor. In contrast, we introduce a new approach based on reshaping the search distribution, which leads to substantial gains over random search, both theoretically and empirically. We propose two flavors of reshaping. First, when the distribution of the optimum is some known $P_0$, we propose Recentering, which uses as search distribution a modified version of $P_0$ tightened closer to the center of the domain, in a dimension-dependent and budget-dependent manner. Second, we show that in a wide range of experiments with $P_0$ unknown, using a proposed Cauchy transformation, which simultaneously has a heavier tail (for unbounded hyperparameters) and is closer to the boundaries (for bounded hyperparameters), leads to improved performances. Besides artificial experiments and simple real world tests on clustering or Salmon mappings, we check our proposed methods on expensive artificial intelligence tasks such as attend/infer/repeat, video next frame segmentation forecasting and progressive generative adversarial networks.

In this paper, we propose FedGP, a framework for privacy-preserving data release in the federated learning setting. We use generative adversarial networks, generator components of which are trained by FedAvg algorithm, to draw privacy-preserving artificial data samples and empirically assess the risk of information disclosure. Our experiments show that FedGP is able to generate labelled data of high quality to successfully train and validate supervised models. Finally, we demonstrate that our approach significantly reduces vulnerability of such models to model inversion attacks.

We propose a Reinforcement Learning based approach to approximately solve the Tree Decomposition (TD)problem. TD is a combinatorial problem, which is central to the analysis of graph minor structure and computational complexity, as well as in the algorithms of probabilistic inference, register allocation, and other practical tasks. Recently, it has been shown that combinatorial problems can be successively solved by learned heuristics. However, the majority of existing works do not address the question of the generalization of learning-based solutions. Our model is based on the graph convolution neural network (GCN) for learning graph representations. We show that the agent builton GCN and trained on a single graph using an Actor-Critic method can efficiently generalize to real-world TD problem instances. We establish that our method successfully generalizes from small graphs, where TD can be found by exact algorithms, to large instances of practical interest, while still having very low time-to-solution. On the other hand, the agent-based approach surpasses all greedy heuristics by the quality of the solution.

Approximate nearest neighbor search is a classic algorithmic problem where the goal is to design an efficient index structure for fast approximate nearest neighbor queries. We show that it can be framed as a classification problem and solved by training a suitable multi-label classifier and using it as an index. Compared to the existing algorithms, this supervised learning approach has several advantages: it enables adapting an index to the query distribution when the query distribution and the corpus distribution differ; it allows using training sets larger than the corpus; and in principle it enables using any multi-label classifier for approximate nearest neighbor search. We demonstrate these advantages on multiple synthetic and real-world data sets by using a random forest and an ensemble of random projection trees as the base classifiers. Introduction In k -nearest neighbor ( k -nn) search, k points that are nearest to the query point are retrieved from the corpus. Approximate nearest neighbor search is used to speed up k -nn search in applications where fast response times are critical, such as in computer vision, robotics, and recommendation systems. Traditionally, approximate nearest neighbor search is approached as a problem in algorithms and data structures. Space-partitioning methods--trees, hashing, and quantization--divide the space according to a geometric criterion. For instance, k -d trees (Bentley 1975) and principal component trees (McNames 2001) are grown by hierarchically partitioning the space along the maximum variance directions of the corpus.

Modal regression is aimed at estimating the global mode (i.e., global maximum) of the conditional density function of the output variable given input variables, and has led to regression methods robust against heavy-tailed or skewed noises. The conditional mode is often estimated through maximization of the modal regression risk (MRR). In order to apply a gradient method for the maximization, the fundamental challenge is accurate approximation of the gradient of MRR, not MRR itself. To overcome this challenge, in this paper, we take a novel approach of directly approximating the gradient of MRR. To approximate the gradient, we develop kernelized and neural-network-based versions of the least-squares log-density derivative estimator, which directly approximates the derivative of the log-density without density estimation. With direct approximation of the MRR gradient, we first propose a modal regression method with kernels, and derive a new parameter update rule based on a fixed-point method. Then, the derived update rule is theoretically proved to have a monotonic hill-climbing property towards the conditional mode. Furthermore, we indicate that our approach of directly approximating the gradient is compatible with recent sophisticated stochastic gradient methods (e.g., Adam), and then propose another modal regression method based on neural networks. Finally, the superior performance of the proposed methods is demonstrated on various artificial and benchmark datasets.

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have proposed to use deep neural networks as a more expressive class of basis functions for calculating the Koopman operators. These approaches, however, assume a fixed dimensional state space; they are therefore not applicable to scenarios with a variable number of objects. In this paper, we propose to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The learned dynamics can quickly adapt to new environments of unknown physical parameters and produce control signals to achieve a specified goal. Our experiments on manipulating ropes and controlling soft robots show that the proposed method has better efficiency and generalization ability than existing baselines.