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2019


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Limitations of the empirical Fisher approximation for natural gradient descent

Kunstner, F., Hennig, P., Balles, L.

Advances in Neural Information Processing Systems 32, pages: 4158-4169, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

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link (url) [BibTex]

2019


link (url) [BibTex]


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Convergence Guarantees for Adaptive Bayesian Quadrature Methods

Kanagawa, M., Hennig, P.

Advances in Neural Information Processing Systems 32, pages: 6234-6245, (Editors: H. Wallach and H. Larochelle and A. Beygelzimer and F. d’Alché-Buc and E. Fox and R. Garnett), Curran Associates, Inc., 33rd Annual Conference on Neural Information Processing Systems, December 2019 (conference)

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link (url) [BibTex]

link (url) [BibTex]


Soft Continuous Surface for Micromanipulation driven by Light-controlled Hydrogels
Soft Continuous Surface for Micromanipulation driven by Light-controlled Hydrogels

Choi, E., Jeong, H., Qiu, T., Fischer, P., Palagi, S.

4th IEEE International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), July 2019 (conference)

Abstract
Remotely controlled, automated actuation and manipulation at the microscale is essential for a number of micro-manufacturing, biology, and lab-on-a-chip applications. To transport and manipulate micro-objects, arrays of remotely controlled micro-actuators are required, which, in turn, typically require complex and expensive solid-state chips. Here, we show that a continuous surface can function as a highly parallel, many-degree of freedom, wirelessly-controlled microactuator with seamless deformation. The soft continuous surface is based on a hydrogel that undergoes a volume change in response to applied light. The fabrication of the hydrogels and the characterization of their optical and thermomechanical behaviors are reported. The temperature-dependent localized deformation of the hydrogel is also investigated by numerical simulations. Static and dynamic deformations are obtained in the soft material by projecting light fields at high spatial resolution onto the surface. By controlling such deformations in open loop and especially closed loop, automated photoactuation is achieved. The surface deformations are then exploited to examine how inert microbeads can be manipulated autonomously on the surface. We believe that the proposed approach suggests ways to implement universal 2D micromanipulation schemes that can be useful for automation in microfabrication and lab-on-a-chip applications.

pf

[BibTex]

[BibTex]


Soft Phantom for the Training of Renal Calculi Diagnostics and  Lithotripsy
Soft Phantom for the Training of Renal Calculi Diagnostics and Lithotripsy

Li., D., Suarez-Ibarrola, R., Choi, E., Jeong, M., Gratzke, C., Miernik, A., Fischer, P., Qiu, T.

41st Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), July 2019 (conference)

Abstract
Organ models are important for medical training and surgical planning. With the fast development of additive fabrication technologies, including 3D printing, the fabrication of 3D organ phantoms with precise anatomical features becomes possible. Here, we develop the first high-resolution kidney phantom based on soft material assembly, by combining 3D printing and polymer molding techniques. The phantom exhibits both the detailed anatomy of a human kidney and the elasticity of soft tissues. The phantom assembly can be separated into two parts on the coronal plane, thus large renal calculi are readily placed at any desired location of the calyx. With our sealing method, the assembled phantom withstands a hydraulic pressure that is four times the normal intrarenal pressure, thus it allows the simulation of medical procedures under realistic pressure conditions. The medical diagnostics of the renal calculi is performed by multiple imaging modalities, including X-ray, ultrasound imaging and endoscopy. The endoscopic lithotripsy is also successfully performed on the phantom. The use of a multifunctional soft phantom assembly thus shows great promise for the simulation of minimally invasive medical procedures under realistic conditions.

pf

[BibTex]

[BibTex]


A Magnetic Actuation System for the  Active Microrheology in Soft Biomaterials
A Magnetic Actuation System for the Active Microrheology in Soft Biomaterials

Jeong, M., Choi, E., Li., D., Palagi, S., Fischer, P., Qiu, T.

4th IEEE International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), July 2019 (conference)

Abstract
Microrheology is a key technique to characterize soft materials at small scales. The microprobe is wirelessly actuated and therefore typically only low forces or torques can be applied, which limits the range of the applied strain. Here, we report a new magnetic actuation system for microrheology consisting of an array of rotating permanent magnets, which achieves a rotating magnetic field with a spatially homogeneous high field strength of ~100 mT in a working volume of ~20×20×20 mm3. Compared to a traditional electromagnetic coil system, the permanent magnet assembly is portable and does not require cooling, and it exerts a large magnetic torque on the microprobe that is an order of magnitude higher than previous setups. Experimental results demonstrate that the measurement range of the soft gels’ elasticity covers at least five orders of magnitude. With the large actuation torque, it is also possible to study the fracture mechanics of soft biomaterials at small scales.

pf

[BibTex]

[BibTex]


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DeepOBS: A Deep Learning Optimizer Benchmark Suite

Schneider, F., Balles, L., Hennig, P.

7th International Conference on Learning Representations (ICLR), May 2019 (conference)

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link (url) [BibTex]

link (url) [BibTex]


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Fast and Robust Shortest Paths on Manifolds Learned from Data

Arvanitidis, G., Hauberg, S., Hennig, P., Schober, M.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1506-1515, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization
Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization

de Roos, F., Hennig, P.

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 89, pages: 1448-1457, (Editors: Kamalika Chaudhuri and Masashi Sugiyama), PMLR, April 2019 (conference)

Abstract
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dominate contemporary machine learning, however, this approach is not readily available. We propose an iterative algorithm inspired by classic iterative linear solvers that uses a probabilistic model to actively infer a pre-conditioner in situations where Hessian-projections can only be constructed with strong Gaussian noise. The algorithm is empirically demonstrated to efficiently construct effective pre-conditioners for stochastic gradient descent and its variants. Experiments on problems of comparably low dimensionality show improved convergence. In very high-dimensional problems, such as those encountered in deep learning, the pre-conditioner effectively becomes an automatic learning-rate adaptation scheme, which we also empirically show to work well.

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PDF link (url) [BibTex]

PDF link (url) [BibTex]

2017


On the Design of {LQR} Kernels for Efficient Controller Learning
On the Design of LQR Kernels for Efficient Controller Learning

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

Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), pages: 5193-5200, IEEE, IEEE Conference on Decision and Control, December 2017 (conference)

Abstract
Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

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arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]

2017


arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]


Coupling Adaptive Batch Sizes with Learning Rates
Coupling Adaptive Batch Sizes with Learning Rates

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

In Proceedings Conference on Uncertainty in Artificial Intelligence (UAI) 2017, pages: 410-419, (Editors: Gal Elidan and Kristian Kersting), Association for Uncertainty in Artificial Intelligence (AUAI), Conference on Uncertainty in Artificial Intelligence (UAI), August 2017 (inproceedings)

Abstract
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.

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Code link (url) Project Page [BibTex]

Code link (url) Project Page [BibTex]


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Dynamic Time-of-Flight

Schober, M., Adam, A., Yair, O., Mazor, S., Nowozin, S.

Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, pages: 170-179, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (conference)

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DOI [BibTex]

DOI [BibTex]


Locomotion of light-driven soft microrobots through a hydrogel via local melting
Locomotion of light-driven soft microrobots through a hydrogel via local melting

Palagi, S., Mark, A. G., Melde, K., Qiu, T., Zeng, H., Parmeggiani, C., Martella, D., Wiersma, D. S., Fischer, P.

In 2017 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), pages: 1-5, July 2017 (inproceedings)

Abstract
Soft mobile microrobots whose deformation can be directly controlled by an external field can adapt to move in different environments. This is the case for the light-driven microrobots based on liquid-crystal elastomers (LCEs). Here we show that the soft microrobots can move through an agarose hydrogel by means of light-controlled travelling-wave motions. This is achieved by exploiting the inherent rise of the LCE temperature above the melting temperature of the agarose gel, which facilitates penetration of the microrobot through the hydrogel. The locomotion performance is investigated as a function of the travelling-wave parameters, showing that effective propulsion can be obtained by adapting the generated motion to the specific environmental conditions.

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DOI [BibTex]

DOI [BibTex]


Virtual vs. {R}eal: Trading Off Simulations and Physical Experiments in Reinforcement Learning with {B}ayesian Optimization
Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization

Marco, A., Berkenkamp, F., Hennig, P., Schoellig, A. P., Krause, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 1557-1563, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

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PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]

PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]


Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets

Klein, A., Falkner, S., Bartels, S., Hennig, P., Hutter, F.

Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS 2017), 54, pages: 528-536, Proceedings of Machine Learning Research, (Editors: Sign, Aarti and Zhu, Jerry), PMLR, April 2017 (conference)

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pdf link (url) Project Page [BibTex]

pdf link (url) Project Page [BibTex]


Wireless micro-robots for endoscopic applications in urology
Wireless micro-robots for endoscopic applications in urology

Adams, F., Qiu, T., Mark, A. G., Melde, K., Palagi, S., Miernik, A., Fischer, P.

In Eur Urol Suppl, 16(3):e1914, March 2017 (inproceedings)

Abstract
Endoscopy is an essential and common method for both diagnostics and therapy in Urology. Current flexible endoscope is normally cable-driven, thus it is hard to be miniaturized and its reachability is restricted as only one bending section near the tip with one degree of freedom (DoF) is allowed. Recent progresses in micro-robotics offer a unique opportunity for medical inspections in minimally invasive surgery. Micro-robots are active devices that has a feature size smaller than one millimeter and can normally be actuated and controlled wirelessly. Magnetically actuated micro-robots have been demonstrated to propel through biological fluids.Here, we report a novel micro robotic arm, which is actuated wirelessly by ultrasound. It works as a miniaturized endoscope with a side length of ~1 mm, which fits through the 3 Fr. tool channel of a cystoscope, and successfully performs an active cystoscopy in a rabbit bladder.

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link (url) DOI [BibTex]

2016


Soft continuous microrobots with multiple intrinsic degrees of freedom
Soft continuous microrobots with multiple intrinsic degrees of freedom

Palagi, S., Mark, A. G., Melde, K., Zeng, H., Parmeggiani, C., Martella, D., Wiersma, D. S., Fischer, P.

In 2016 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), pages: 1-5, July 2016 (inproceedings)

Abstract
One of the main challenges in the development of microrobots, i.e. robots at the sub-millimeter scale, is the difficulty of adopting traditional solutions for power, control and, especially, actuation. As a result, most current microrobots are directly manipulated by external fields, and possess only a few passive degrees of freedom (DOFs). We have reported a strategy that enables embodiment, remote powering and control of a large number of DOFs in mobile soft microrobots. These consist of photo-responsive materials, such that the actuation of their soft continuous body can be selectively and dynamically controlled by structured light fields. Here we use finite-element modelling to evaluate the effective number of DOFs that are addressable in our microrobots. We also demonstrate that by this flexible approach different actuation patterns can be obtained, and thus different locomotion performances can be achieved within the very same microrobot. The reported results confirm the versatility of the proposed approach, which allows for easy application-specific optimization and online reconfiguration of the microrobot's behavior. Such versatility will enable advanced applications of robotics and automation at the micro scale.

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DOI [BibTex]

2016


DOI [BibTex]


Wireless actuator based on ultrasonic bubble streaming
Wireless actuator based on ultrasonic bubble streaming

Qiu, T., Palagi, S., Mark, A. G., Melde, K., Fischer, P.

In 2016 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS), pages: 1-5, July 2016 (inproceedings)

Abstract
Miniaturized actuators are a key element for the manipulation and automation at small scales. Here, we propose a new miniaturized actuator, which consists of an array of micro gas bubbles immersed in a fluid. Under ultrasonic excitation, the oscillation of micro gas bubbles results in acoustic streaming and provides a propulsive force that drives the actuator. The actuator was fabricated by lithography and fluidic streaming was observed under ultrasound excitation. Theoretical modelling and numerical simulations were carried out to show that lowing the surface tension results in a larger amplitude of the bubble oscillation, and thus leads to a higher propulsive force. Experimental results also demonstrate that the propulsive force increases 3.5 times when the surface tension is lowered by adding a surfactant. An actuator with a 4×4 mm 2 surface area provides a driving force of about 0.46 mN, suggesting that it is possible to be used as a wireless actuator for small-scale robots and medical instruments.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


Active Uncertainty Calibration in Bayesian ODE Solvers
Active Uncertainty Calibration in Bayesian ODE Solvers

Kersting, H., Hennig, P.

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

Abstract
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al.~introduced a sampling-based class of methods that are `well-calibrated' in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the other hand, Schober et al.~pointed out a precise connection between classic Runge-Kutta ODE solvers and Gaussian filters, which gives only a rough probabilistic calibration, but at negligible cost overhead. By formulating the solution of ODEs as approximate inference in linear Gaussian SDEs, we investigate a range of probabilistic ODE solvers, that bridge the trade-off between computational cost and probabilistic calibration, and identify the inaccurate gradient measurement as the crucial source of uncertainty. We propose the novel filtering-based method Bayesian Quadrature filtering (BQF) which uses Bayesian quadrature to actively learn the imprecision in the gradient measurement by collecting multiple gradient evaluations.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


Automatic {LQR} Tuning Based on {G}aussian Process Global Optimization
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), pages: 270-277, IEEE, IEEE International Conference on Robotics and Automation, May 2016 (inproceedings)

Abstract
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.

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Video PDF DOI Project Page [BibTex]

Video PDF DOI Project Page [BibTex]


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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), 51, pages: 648-657, JMLR Workshop and Conference Proceedings, (Editors: Gretton, A. and Robert, C. C.), May 2016 (conference)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Auxetic Metamaterial Simplifies Soft Robot Design
Auxetic Metamaterial Simplifies Soft Robot Design

Mark, A. G., Palagi, S., Qiu, T., Fischer, P.

In 2016 IEEE Int. Conf. on Robotics and Automation (ICRA), pages: 4951-4956, May 2016 (inproceedings)

Abstract
Soft materials are being adopted in robotics in order to facilitate biomedical applications and in order to achieve simpler and more capable robots. One route to simplification is to design the robot's body using `smart materials' that carry the burden of control and actuation. Metamaterials enable just such rational design of the material properties. Here we present a soft robot that exploits mechanical metamaterials for the intrinsic synchronization of two passive clutches which contact its travel surface. Doing so allows it to move through an enclosed passage with an inchworm motion propelled by a single actuator. Our soft robot consists of two 3D-printed metamaterials that implement auxetic and normal elastic properties. The design, fabrication and characterization of the metamaterials are described. In addition, a working soft robot is presented. Since the synchronization mechanism is a feature of the robot's material body, we believe that the proposed design will enable compliant and robust implementations that scale well with miniaturization.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


Probabilistic Approximate Least-Squares
Probabilistic Approximate Least-Squares

Bartels, S., Hennig, P.

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

Abstract
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.

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link (url) Project Page Project Page [BibTex]

link (url) Project Page Project Page [BibTex]


Towards Photo-Induced Swimming: Actuation of Liquid Crystalline  Elastomer in Water
Towards Photo-Induced Swimming: Actuation of Liquid Crystalline Elastomer in Water

cerretti, G., Martella, D., Zeng, H., Parmeggiani, C., Palagi, S., Mark, A. G., Melde, K., Qiu, T., Fischer, P., Wiersma, D.

In Proc. of SPIE 9738, pages: Laser 3D Manufacturing III, 97380T, April 2016 (inproceedings)

Abstract
Liquid Crystalline Elastomers (LCEs) are very promising smart materials that can be made sensitive to different external stimuli, such as heat, pH, humidity and light, by changing their chemical composition. In this paper we report the implementation of a nematically aligned LCE actuator able to undergo large light-induced deformations. We prove that this property is still present even when the actuator is submerged in fresh water. Thanks to the presence of azo-dye moieties, capable of going through a reversible trans-cis photo-isomerization, and by applying light with two different wavelengths we managed to control the bending of such actuator in the liquid environment. The reported results represent the first step towards swimming microdevices powered by light.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2010


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Using an Infinite Von Mises-Fisher Mixture Model to Cluster Treatment Beam Directions in External Radiation Therapy

Bangert, M., Hennig, P., Oelfke, U.

In pages: 746-751 , (Editors: Draghici, S. , T.M. Khoshgoftaar, V. Palade, W. Pedrycz, M.A. Wani, X. Zhu), IEEE, Piscataway, NJ, USA, Ninth International Conference on Machine Learning and Applications (ICMLA), December 2010 (inproceedings)

Abstract
We present a method for fully automated selection of treatment beam ensembles for external radiation therapy. We reformulate the beam angle selection problem as a clustering problem of locally ideal beam orientations distributed on the unit sphere. For this purpose we construct an infinite mixture of von Mises-Fisher distributions, which is suited in general for density estimation from data on the D-dimensional sphere. Using a nonparametric Dirichlet process prior, our model infers probability distributions over both the number of clusters and their parameter values. We describe an efficient Markov chain Monte Carlo inference algorithm for posterior inference from experimental data in this model. The performance of the suggested beam angle selection framework is illustrated for one intra-cranial, pancreas, and prostate case each. The infinite von Mises-Fisher mixture model (iMFMM) creates between 18 and 32 clusters, depending on the patient anatomy. This suggests to use the iMFMM directly for beam ensemble selection in robotic radio surgery, or to generate low-dimensional input for both subsequent optimization of trajectories for arc therapy and beam ensemble selection for conventional radiation therapy.

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Web DOI [BibTex]

2010


Web DOI [BibTex]


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Coherent Inference on Optimal Play in Game Trees

Hennig, P., Stern, D., Graepel, T.

In JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010, pages: 326-333, (Editors: Teh, Y.W. , M. Titterington ), JMLR, Cambridge, MA, USA, Thirteenth International Conference on Artificial Intelligence and Statistics, May 2010 (inproceedings)

Abstract
Round-based games are an instance of discrete planning problems. Some of the best contemporary game tree search algorithms use random roll-outs as data. Relying on a good policy, they learn on-policy values by propagating information upwards in the tree, but not between sibling nodes. Here, we present a generative model and a corresponding approximate message passing scheme for inference on the optimal, off-policy value of nodes in smooth AND/OR trees, given random roll-outs. The crucial insight is that the distribution of values in game trees is not completely arbitrary. We define a generative model of the on-policy values using a latent score for each state, representing the value under the random roll-out policy. Inference on the values under the optimal policy separates into an inductive, pre-data step and a deductive, post-data part. Both can be solved approximately with Expectation Propagation, allowing off-policy value inference for any node in the (exponentially big) tree in linear time.

ei pn

PDF Web [BibTex]

PDF Web [BibTex]