Next, we are going to cover several stages in one step, all are related to each other and it will make more sense. Previously we have seen the methods for signaling the beginning of a run and of an epoch. In every epoch, we have to iterate over the entire dataset, for various reasons related to both computational and convergence optimizations we do so in batches (mini-batch stochastic gradient descent). As such we have to log some information related to this step to our RunManager, which will help us to compute the overall loss and the accuracy for the entire epoch. Once the epoch finishes we have to compute the aforementioned metrics, save them to the local collection and log them to Tensorboard.

The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example, Joen & Van Roy (arXiv:2203.00246) demonstrate that, when data is generated by a ReLU teacher network with $W$ parameters, an optimal learner needs only $\tilde{O}(W/\epsilon)$ samples to attain expected error $\epsilon$. However, existing computational theory suggests that, even for single-hidden-layer teacher networks, to attain small error for all such teacher networks, the computation required to achieve this sample complexity is intractable. In this work, we fit single-hidden-layer neural networks to data generated by single-hidden-layer ReLU teacher networks with parameters drawn from a natural distribution. We demonstrate that stochastic gradient descent (SGD) with automated width selection attains small expected error with a number of samples and total number of queries both nearly linear in the input dimension and width. This suggests that SGD nearly achieves the information-theoretic sample complexity bounds of Joen & Van Roy (arXiv:2203.00246) in a computationally efficient manner. An important difference between our positive empirical results and the negative theoretical results is that the latter address worst-case error of deterministic algorithms, while our analysis centers on expected error of a stochastic algorithm.

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions and large datasets. We address the bottleneck problem arising when using both shared and distributed memory. Typically, the former is bounded by limited computation resources and bandwidth whereas the latter suffers from communication overheads. We propose a unified distributed and parallel implementation of SGD (named DPSGD) that relies on both asynchronous distribution and lock-free parallelism. By combining two strategies into a unified framework, DPSGD is able to strike a better trade-off between local computation and communication. The convergence properties of DPSGD are studied for non-convex problems such as those arising in statistical modelling and machine learning. Our theoretical analysis shows that DPSGD leads to speed-up with respect to the number of cores and number of workers while guaranteeing an asymptotic convergence rate of $O(1/\sqrt{T})$ given that the number of cores is bounded by $T^{1/4}$ and the number of workers is bounded by $T^{1/2}$ where $T$ is the number of iterations. The potential gains that can be achieved by DPSGD are demonstrated empirically on a stochastic variational inference problem (Latent Dirichlet Allocation) and on a deep reinforcement learning (DRL) problem (advantage actor critic - A2C) resulting in two algorithms: DPSVI and HSA2C. Empirical results validate our theoretical findings. Comparative studies are conducted to show the performance of the proposed DPSGD against the state-of-the-art DRL algorithms.

The rapid expansion of data worldwide invites the need for more distributed solutions in order to apply machine learning on a much wider scale. The resultant distributed learning systems can have various degrees of centralization. In this work, we demonstrate our solution FLoBC for building a generic decentralized federated learning system using blockchain technology, accommodating any machine learning model that is compatible with gradient descent optimization. We present our system design comprising the two decentralized actors: trainer and validator, alongside our methodology for ensuring reliable and efficient operation of said system. Finally, we utilize FLoBC as an experimental sandbox to compare and contrast the effects of trainer-to-validator ratio, reward-penalty policy, and model synchronization schemes on the overall system performance, ultimately showing by example that a decentralized federated learning system is indeed a feasible alternative to more centralized architectures.

Models need to be trained with privacy-preserving learning algorithms to prevent leakage of possibly sensitive information contained in their training data. However, canonical algorithms like differentially private stochastic gradient descent (DP-SGD) do not benefit from model scale in the same way as non-private learning. This manifests itself in the form of unappealing tradeoffs between privacy and utility (accuracy) when using DP-SGD on complex tasks. To remediate this tension, a paradigm is emerging: fine-tuning with differential privacy from a model pretrained on public (i.e., non-sensitive) training data. In this work, we identify an oversight of existing approaches for differentially private fine tuning. They do not tailor the fine-tuning approach to the specifics of learning with privacy. Our main result is to show how carefully selecting the layers being fine-tuned in the pretrained neural network allows us to establish new state-of-the-art tradeoffs between privacy and accuracy. For instance, we achieve 77.9% accuracy for $(\varepsilon, \delta)=(2, 10^{-5})$ on CIFAR-100 for a model pretrained on ImageNet. Our work calls for additional hyperparameter search to configure the differentially private fine-tuning procedure itself.

Continual learning in neural networks suffers from a phenomenon called catastrophic forgetting, in which a network quickly forgets what was learned in a previous task. The human brain, however, is able to continually learn new tasks and accumulate knowledge throughout life. Neuroscience findings suggest that continual learning success in the human brain is potentially associated with its modular structure and memory consolidation mechanisms. In this paper we propose a novel topological regularization that penalizes cycle structure in a neural network during training using principled theory from persistent homology and optimal transport. The penalty encourages the network to learn modular structure during training. The penalization is based on the closed-form expressions of the Wasserstein distance and barycenter for the topological features of a 1-skeleton representation for the network. Our topological continual learning method combines the proposed regularization with a tiny episodic memory to mitigate forgetting. We demonstrate that our method is effective in both shallow and deep network architectures for multiple image classification datasets.

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One of these approaches is reducing the gradient variance through adaptive sampling to solve large-scale optimization's empirical risk minimization (ERM) problems. In this paper, we will explore how starting with a small sample and then geometrically increasing it and using the solution of the previous sample ERM to compute the new ERM. This will solve ERM problems with first-order optimization algorithms of sublinear convergence but with lower computational complexity. This paper starts with theoretical proof of the approach, followed by two experiments comparing the gradient descent with the adaptive sampling of the gradient descent and ADAM with adaptive sampling ADAM on different datasets.

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 information brought in by the control variates. The quadrature points and weights do not depend on the integrand, a computational advantage in case of multiple integrands. Moreover, the target density needs to be known only up to a multiplicative constant. Our main result is a non-asymptotic bound on the probabilistic error of the procedure. The bound proves that for improving the estimate's accuracy, the benefits from adaptive importance sampling and control variates can be combined. The good behavior of the method is illustrated empirically on synthetic examples and real-world data for Bayesian linear regression.

Bayesian optimization (BO) is a popular method for efficiently inferring optima of an expensive black-box function via a sequence of queries. Existing information-theoretic BO procedures aim to make queries that most reduce the uncertainty about optima, where the uncertainty is captured by Shannon entropy. However, an optimal measure of uncertainty would, ideally, factor in how we intend to use the inferred quantity in some downstream procedure. In this paper, we instead consider a generalization of Shannon entropy from work in statistical decision theory (DeGroot 1962, Rao 1984), which contains a broad class of uncertainty measures parameterized by a problem-specific loss function corresponding to a downstream task. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures such as knowledge gradient, expected improvement, and entropy search. We then show how alternative choices for the loss yield a flexible family of acquisition functions that can be customized for use in novel optimization settings. Additionally, we develop gradient-based methods to efficiently optimize our proposed family of acquisition functions, and demonstrate strong empirical performance on a diverse set of sequential decision making tasks, including variants of top-$k$ optimization, multi-level set estimation, and sequence search.

Adversarial training (AT) is a widely recognized defense mechanism to gain the robustness of deep neural networks against adversarial attacks. It is built on min-max optimization (MMO), where the minimizer (i.e., defender) seeks a robust model to minimize the worst-case training loss in the presence of adversarial examples crafted by the maximizer (i.e., attacker). However, the conventional MMO method makes AT hard to scale. Thus, Fast-AT (Wong et al., 2020) and other recent algorithms attempt to simplify MMO by replacing its maximization step with the single gradient sign-based attack generation step. Although easy to implement, Fast-AT lacks theoretical guarantees, and its empirical performance is unsatisfactory due to the issue of robust catastrophic overfitting when training with strong adversaries. In this paper, we advance Fast-AT from the fresh perspective of bi-level optimization (BLO). We first show that the commonly-used Fast-AT is equivalent to using a stochastic gradient algorithm to solve a linearized BLO problem involving a sign operation. However, the discrete nature of the sign operation makes it difficult to understand the algorithm performance. Inspired by BLO, we design and analyze a new set of robust training algorithms termed Fast Bi-level AT (Fast-BAT), which effectively defends sign-based projected gradient descent (PGD) attacks without using any gradient sign method or explicit robust regularization. In practice, we show our method yields substantial robustness improvements over baselines across multiple models and datasets. Codes are available at https://github.com/OPTML-Group/Fast-BAT.