Information-Theoretic Trust Regions for Stochastic Gradient-Based Optimization

Stochastic gradient-based optimization is crucial to optimize neural networks. While popular approaches heuristically adapt the step size and direction by rescaling gradients, a more principled approach to improve optimizers requires second-order information. Such methods precondition the gradient using the objective's Hessian. Yet, computing the Hessian is usually expensive and effectively using second-order information in the stochastic gradient setting is non-trivial. We propose using Information-Theoretic Trust Region Optimization (arTuRO) for improved updates with uncertain second-order information. By modeling the network parameters as a Gaussian distribution and using a Kullback-Leibler divergence-based trust region, our approach takes bounded steps accounting for the objective's curvature and uncertainty in the parameters. Before each update, it solves the trust region problem for an optimal step size, resulting in a more stable and faster optimization process. We approximate the diagonal elements of the Hessian from stochastic gradients using a simple recursive least squares approach, constructing a model of the expected Hessian over time using only first-order information. We show that arTuRO combines the fast convergence of adaptive moment-based optimization with the generalization capabilities of SGD

Information-Theoretic Trust Regions for Stochastic Gradient-Based Optimization

Stochastic gradient-based optimization is crucial to optimize neural networks. While popular approaches heuristically adapt the step size and direction by rescaling gradients, a more principled approach to improve optimizers requires second-order information. Such methods precondition the gradient using the objective’s Hessian. Yet, computing the Hessian is usually expensive and effectively using second-order information in the stochastic gradient setting is non-trivial. We propose using Information-Theoretic Trust Region Optimization (arTuRO) for improved updates with uncertain second-order information. By modeling the network parameters as a Gaussian distribution and using a Kullback-Leibler divergence-based trust region, our approach takes bounded steps accounting for the objective’s curvature and uncertainty in the parameters. Before each update, it solves the trust region problem for an optimal step size, resulting in a more stable and faster optimization process. We approximate the diagonal elements of the Hessian from stochastic gradients using a simple recursive least squares approach, constructing a model of the expected Hessian over time using only first-order information. We show that arTuRO combines the fast convergence of adaptive moment-based optimization with the generalization capabilities of SGD

Swarm Reinforcement Learning For Adaptive Mesh Refinement

Adaptive Mesh Refinement (AMR) enhances the Finite Element Method, an important technique for simulating complex problems in engineering, by dynamically refining mesh regions, enabling a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on heuristics or expensive error estimators, hindering their use for complex simulations. Recent learning-based AMR methods tackle these issues, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate our approach, Adaptive Swarm Mesh Refinement (ASMR), on challenging refinement tasks. Our approach learns reliable and efficient refinement strategies that can robustly generalize to different domains during inference. Additionally, it achieves a speedup of up to $2$ orders of magnitude compared to uniform refinements in more demanding simulations. We outperform learned baselines and heuristics, achieving a refinement quality that is on par with costly error-based oracle AMR strategies

Swarm Reinforcement Learning For Adaptive Mesh Refinement

The Finite Element Method, an important technique in engineering, is aided by Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow for a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on task-specific heuristics or expensive error estimators, hindering their use for complex simulations. Recent learned AMR methods tackle these problems, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate the effectiveness of our approach, Adaptive Swarm Mesh Refinement (ASMR), showing that it learns reliable, scalable, and efficient refinement strategies on a set of challenging problems. Our approach significantly speeds up computation, achieving up to 30-fold improvement compared to uniform refinements in complex simulations. Additionally, we outperform learned baselines and achieve a refinement quality that is on par with a traditional error-based AMR strategy without expensive oracle information about the error signal.Comment: Version 1 of this paper is a preliminary workshop version that was accepted as a workshop paper in the ICLR 2023 Workshop on Physics for Machine Learnin

Preventing traffic accidents with in-vehicle decision support systems - The impact of accident hotspot warnings on driver behaviour

ISSN:0167-9236ISSN:1873-579

A Unified Perspective on Natural Gradient Variational Inference with Gaussian Mixture Models

Variational inference with Gaussian mixture models (GMMs) enables learning of highly tractable yet multi-modal approximations of intractable target distributions with up to a few hundred dimensions. The two currently most effective methods for GMM-based variational inference, VIPS and iBayes-GMM, both employ independent natural gradient updates for the individual components and their weights. We show for the first time, that their derived updates are equivalent, although their practical implementations and theoretical guarantees differ. We identify several design choices that distinguish both approaches, namely with respect to sample selection, natural gradient estimation, stepsize adaptation, and whether trust regions are enforced or the number of components adapted. We argue that for both approaches, the quality of the learned approximations can heavily suffer from the respective design choices: By updating the individual components using samples from the mixture model, iBayes-GMM often fails to produce meaningful updates to low-weight components, and by using a zero-order method for estimating the natural gradient, VIPS scales badly to higher-dimensional problems. Furthermore, we show that information-geometric trust-regions (used by VIPS) are effective even when using first-order natural gradient estimates, and often outperform the improved Bayesian learning rule (iBLR) update used by iBayes-GMM. We systematically evaluate the effects of design choices and show that a hybrid approach significantly outperforms both prior works. Along with this work, we publish our highly modular and efficient implementation for natural gradient variational inference with Gaussian mixture models, which supports 432 different combinations of design choices, facilitates the reproduction of all our experiments, and may prove valuable for the practitioner.Comment: This version corresponds to the camera ready version published at Transactions of Machine Learning Research (TMLR). https://openreview.net/forum?id=tLBjsX4tj

ALICE addentum to the Technical Design Report of the time of flight system (TOF)

ALIC