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Register a new userMetaGrad: Adaptation using Multiple Learning Rates in Online Learning
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We provide a new adaptive method for online convex optimization, MetaGrad, that is robust to general convex losses but achieves faster rates for a broad class of special functions, including exp-concave and strongly convex functions, but also various types of stochastic and non-stochastic functions without any curvature. We prove this by drawing a connection to the Bernstein condition, which is known to imply fast rates in offline statistical learning. MetaGrad further adapts automatically to the size of the gradients. Its main feature is that it simultaneously considers multiple learning rates, which are weighted directly proportional to their empirical performance on the data using a new meta-algorithm. We provide thr
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In online convex optimization it is well known that certain subclasses of objective functions are much easier than arbitrary convex functions. We are interested in designing adaptive methods that can automatically get fast rates in as many such subclasses as possible, without any manual tuning. Previous adaptive methods are able to interpolate between strongly convex and general convex functions. We present a new method, MetaGrad, that adapts to a much broader class of functions, including exp-concave and strongly convex functions, but also various types of stochastic and non-stochastic functions without any curvature. For instance, MetaGrad can achieve logarithmic regret on the unregularized hinge loss, even though it has no curvature, if the data come from a favourable probability distribution. MetaGrads main feature is that it simultaneously considers multiple learning rates. Unlike previous methods with provable regret guarantees, however, its learning rates are not monotonically decreasing over time and are not tuned based on a theoretically derived bound on the regret. Instead, they are weighted directly proportional to their empirical performance on the data using a tilted exponential weights master algorithm.
We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up in the design of such adaptive algorithms is to calibrate a so-called step-size or learning rate hyperparameter depending on variance, gradient norms, etc. A recent technique promises to overcome this difficulty by maintaining multiple learning rates in parallel. This technique has been applied in the MetaGrad algorithm for online convex optimization and the Squint algorithm for prediction with expert advice. However, in both cases the user still has to provide in advance a Lipschitz hyperparameter that bounds the norm of the gradients. Although this hyperparameter is typically not available in advance, tuning it correctly is crucial: if it is set too small, the methods may fail completely; but if it is taken too large, performance deteriorates significantly. In the present work we remove this Lipschitz hyperparameter by designing n
We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this hypergradient needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.
Industrial control systems are critical to the operation of industrial facilities, especially for critical infrastructures, such as refineries, power grids, and transportation systems. Similar to other information systems, a significant threat to industrial control systems is the attack from cyberspace---the offensive maneuvers launched by anonymous in the digital world that target computer-based assets with the goal of compromising a systems functions or probing for information. Owing to the importance of industrial control systems, and the possibly devastating consequences of being attacked, significant endeavors have been attempted to secure industrial control systems from cyberattacks. Among them are intrusion detection systems that serve as the first line of defense by monitoring and reporting potentially malicious activities. Classical machine-learning-based intrusion detection methods usually generate prediction models by learning modest-sized training samples all at once. Such approach is not always applicable to industrial control systems, as industrial control systems must process continuous control commands with limited computational resources in a nonstop way. To satisfy such requirements, we propose using online learning to learn prediction models from the controlling data stream. We introduce several state-of-the-art online learning algorithms categorically, and illustrate their efficacies on two typically used testbeds---power system and gas pipeline. Further, we explore a new cost-sensitive online learning algorithm to solve the class-imbalance problem that is pervasive in industrial intrusion detection systems. Our experimental results indicate that the proposed algorithm can achieve an overall improvement in the detection rate of cyberattacks in industrial control systems.
Few-shot meta-learning methods consider the problem of learning new tasks from a small, fixed number of examples, by meta-learning across static data from a set of previous tasks. However, in many real world settings, it is more natural to view the problem as one of minimizing the total amount of supervision --- both the number of examples needed to learn a new task and the amount of data needed for meta-learning. Such a formulation can be studied in a sequential learning setting, where tasks are presented in sequence. When studying meta-learning in this online setting, a critical question arises: can meta-learning improve over the sample complexity and regret of standard empirical risk minimization methods, when considering both meta-training and adaptation together? The answer is particularly non-obvious for meta-learning algorithms with complex bi-level optimizations that may demand large amounts of meta-training data. To answer this question, we extend previous meta-learning algorithms to handle the variable-shot settings that naturally arise in sequential learning: from many-shot learning at the start, to zero-shot learning towards the end. On sequential learning problems, we find that meta-learning solves the full task set with fewer overall labels and achieves greater cumulative performance, compared to standard supervised methods. These results suggest that meta-learning is an important ingredient for building learning systems that continuously learn and improve over a sequence of problems.
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