8 results (BibTeX)

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Coupling Adaptive Batch Sizes with Learning Rates

Balles, L., Romero, J., Hennig, P.

arXiv preprint arXiv:1612.05086, 2016 (article)

Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the stochastic optimization algorithm, though, since it determines the variance of the gradient estimates. This variance also changes over the optimization process; when using a constant batch size, stability and convergence is thus often enforced by means of a (manually tuned) decreasing learning rate schedule. We propose a practical method for dynamic batch size adaptation. It estimates the variance of the stochastic gradients and adapts the batch size to decrease the variance proportionally to the value of the objective function, removing the need for the aforementioned learning rate decrease. In contrast to recent related work, our algorithm couples the batch size to the learning rate, directly reflecting the known relationship between the two. On three image classification benchmarks, our batch size adaptation yields faster optimization convergence, while simultaneously simplifying learning rate tuning. A TensorFlow implementation is available.

Code link (url) [BibTex]

Batch Bayesian Optimization via Local Penalization

González, J., Dai, Z., Hennig, P., Lawrence, N.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), 2016 (conference)

link (url) [BibTex]

link (url) [BibTex]

Active Uncertainty Calibration in Bayesian ODE Solvers

Kersting, H., Hennig, P.

Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence (UAI 2016), pages: 309-318, (Editors: Ihler, A. and Janzing, D.), AUAI Press, 2016 (conference)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

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Probabilistic Approximate Least-Squares

Bartels, S., Hennig, P.

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016), 51, pages: 676-684, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C. ), 2016 (conference)

Least-squares and kernel-ridge / Gaussian process regression are among the foundational algorithms of statistics and machine learning. Famously, the worst-case cost of exact nonparametric regression grows cubically with the data-set size; but a growing number of approximations have been developed that estimate good solutions at lower cost. These algorithms typically return point estimators, without measures of uncertainty. Leveraging recent results casting elementary linear algebra operations as probabilistic inference, we propose a new approximate method for nonparametric least-squares that affords a probabilistic uncertainty estimate over the error between the approximate and exact least-squares solution (this is not the same as the posterior variance of the associated Gaussian process regressor). This allows estimating the error of the least-squares solution on a subset of the data relative to the full-data solution. The uncertainty can be used to control the computational effort invested in the approximation. Our algorithm has linear cost in the data-set size, and a simple formal form, so that it can be implemented with a few lines of code in programming languages with linear algebra functionality.

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

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Automatic LQR Tuning Based on Gaussian Process Global Optimization

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree- of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four- dimensional tuning problems highlight the method’s potential for automatic controller tuning on robotic platforms.

Video PDF DOI Project Page [BibTex]

Video PDF DOI Project Page [BibTex]

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Dual Control for Approximate Bayesian Reinforcement Learning

Klenske, E., Hennig, P.

Journal of Machine Learning Research, 17(127):1-30, 2016 (article)

PDF link (url) Project Page [BibTex]

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Gaussian Process Based Predictive Control for Periodic Error Correction

Klenske, E., Zeilinger, M., Schölkopf, B., Hennig, P.

IEEE Transactions on Control Systems Technology , 24(1):110-121, 2016 (article)

PDF DOI Project Page [BibTex]