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Auto-Supervised Learning in the Bayesian Programming Framework∗

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Auto-Supervised Learning in the Bayesian Programming Framework∗ Auto-supervised learning in the Bayesian Programming Framework∗ Pierre Dangauthier and Pierre Bessier` e and Anne Spalanzani E-Motion INRIA / GRAVIR - CNRS 655 Avenue de l'Europe, Montbonnot 38334 Saint Ismier cedex - France [email protected] Abstract This learning is possible by searching, and exploiting sta- tistical regularities in the sensorimotor space. The exploita- Domestic and real world robotics requires continuous learning of new skills and behaviors to interact with tion of statistical regularities can be seen as the foundation humans. Auto-supervised learning, a compromise be- of learning and is a promising model of cognition (Barlow tween supervised and completely unsupervised learn- 2001). Finding regularities means finding compact data rep- ing, consist in relying on previous knowledge to acquire resentations, with which a system becomes able to general- new skills. We propose here to realize auto-supervised ize and makes sense of its perceptions. learning by exploiting statistical regularities in the sen- sorimotor space of a robot. In our context, it corre- Bayesian Robot Programming sponds to achieve feature selection in a Bayesian pro- Apart from the notion of auto-supervised learning, a domes- gramming framework. We compare several feature se- tic robot perceives abundant, uncertain and often contradic- lection algorithms and validate them on a real robotic experiment. tory information. Sensors and actuators are not perfectly reliable. Therefore, classical determinist programming has been shown to be unable to address real world problems Introduction (Bessiere` et al. 1998). We prefer to use a probabilistic ap- In a real environment, a robot needs to continuously improve proach method called Bayesian Programming. Bayesian its knowledge to interact with humans. It needs to better the Robot Programming is a promising candidate in this con- performance of its previously known skills and to learn new text (Bessiere` & the LAPLACE research Group 2003) and ones. In a complex environment, learning totally new behav- has given several interesting results (Lebeltel et al. 2003) iors probably require human feedback. But there are sim- (Pradalier & Bessiere` 2004). Moreover, Bayesian Inference ple situations where unsupervised, or more precisely auto- is a promising model for understanding animal perception supervised learning, is possible. We study in this article the and cognition (BIBA 2001 2005). case of a robot which improves the use of its body without Bayesian Robot Programming is based on the subjec- any human supervision. In a simple tracking task, the robot tive interpretation of probabilities deeply described by E.T. learns by itself to use its laser sensor (SICK) instead of its Jaynes (Jaynes 2003). A Bayesian program is a probabilistic camera. This is done by searching for correlations in the representation of the relations between sensors and actuators space of its sensor and motor variables during the tracking in order to perform a specified task. behavior. In this framework, a Bayesian programmer starts to de- scribe a task by specifying preliminary knowledge to the Auto-supervised learning robot. Then the robot processes Bayesian inference in order Auto-supervised learning is biologically inspired and is to take a decision regarding its inputs. strongly related to mental development (Weng et al. 2001). Establishing preliminary knowledge can be divided into This way of learning takes place during baby's development, three parts: but also during adulthood. For instance, a beginner strongly • Define relevant variables for the problem; relies on his sight to use a computer keyboard. Then, he • Possibly assume conditional independencies between learns to use his finger sensibility and spatial position to per- them; form the same task. One can say that he learned a new sen- sorimotor behavior thanks to the supervision of his sight. • Choose prior distributions on those variables. ∗ The reader can find detailed examples of non-trivial This work is partially supported by the European Bayesian In- Bayesian programs in (Lebeltel et al. 2003). spired Brain and Artefacts (BIBA) project, by the French National Institute for Research in Computer Science and Control (INRIA), and by the French Research Ministry. Goal Copyright c 2005, American Association for Artificial Intelli- In this work, we present an attempt to automate the creation gence (www.aaai.org). All rights reserved. of a Bayesian program. The “relevant variables” part of a new program will be autonomously discovered under the su- non-zero values, are frequently used to model discrete pervision of another Bayesian program. probability distributions. The initial behavior of the robot is to track a red ball with • Question: Once this program is defined, the goal for the a digital camera. This behavior is controlled by an initial robot is to infer the position of the ball θ : Bayesian program. During a tracking experiment, all sen- sor inputs are recorded, including the direction of the ball. Then, the robot looks for sensors highly correlated with the θ = Argmax P (θjX0 : : : XN ) position of the ball. After that, the robot builds a new track- P (X0 : : : XN θ) ing program with these sensors, and is then able to stare at = Argmax the target without its camera. P (X0 : : : XN ) We present here several algorithms for discovering the rel- N evant variables related to that simple tracking task. = Argmax Y P (Xijθ): i=0 Approach Robotics Once the robot has recorded, for each time step, the position of the ball given by its camera and all other sensor values, the We carried out our experiments on the BibaBot (see Fig.1), problem is reduced to classical supervised learning. Thus, the robot of the BIBA European project (BIBA 2001 the goal is to find the minimal set of variables allowing a 2005). It is a middle sized (1 - 0.5 - 0.5 m) wheeled robot good prediction of the position. equipped with a lot of different sensors. In this work, the Finding relevant variables for good predictions is a well robot stay motionless. known problem in the AI field. In our case, the selected sub- set of variables will be the input of a naive Bayesian clas- sifier(Domingos & Pazzani 1997). This search is therefore called feature selection for machine learning. This article presents different feature selection methods for finding correlations between a variable and the sensor data. We show that our methods enhance the computing time and the recognition rate of the classification. A study of the selected sensors allows us to validate the relevance of our approach regarding the investigation for new sensorimotor modalities. Experiment Presentation The problem is as follows: we have a robot with a lot of dif- ferent sensors (laser range SICK, proximeters, thermometer, odometers, battery level...) and a ball is moving in the hor- izontal plane. The ball position is defined by the angle θ between the ball and the robot's main axe. A set of learn- ing examples is recorded. For each time step, we record θ and the related values of all the sensors. After a learning stage, our robot should be able to guess the position of the Figure 1: The BibaBot Robot. ball knowing its sensor values. The new constructed Bayesian program will be: It is equipped with: • Relevant variables are sensors carrying information about • A Pan-Tilt camera, θ. We denote sensors variables by X , 8i 2 [0 : : : N − 1]. i • A laser scanner (SICK LMS 200 Fig.2) that scans its sur- • Decomposition: The decomposition of the joint proba- roundings in 2D. It gives 360 measures of distance in the bility distribution we have chosen is called naive Bayes horizontal plane. We will consider each laser beam as an model. In our framework, it is reasonable to assume individual sensor. that sensor values are conditionally independent given the • 3 odometry sensors, value of θ. Thus the decomposition is: • 4 bumpers, N−1 • 8 ultrasonic sensors, P (X0 : : : XN−1; θ) = P (θ) Y P (Xijθ): i=0 • 15 infrared proximity sensors. • Priors: We choose Laplace's histograms (Jaynes 2003). • a clock and the battery voltage. Laplace's histograms, which are simple histograms with The experiment is then done in three steps: • It leads to a simpler model of data (Occam Razor argu- ment (Blumer et al. 1987)), • It enhances the classifier performance, speed and general- ity, • It leads to a more comprehensible model and shows con- ditional dependencies between variables. Usually feature selection algorithms remove independent or redundant variables. General feature selection structure It is possible to derive a common architecture from most of the feature selection algorithms (see Fig. 3). These algo- Figure 2: A SICK output, when the robot is placed in a cor- rithms create a subset, evaluate it, and loop until an ending ridor criterion is satisfied (Liu & Motoda 1998). Finally the sub- set found is validated with the classifier algorithm on real data. • Firstly the visual tracking program is launched and a red ball is moving in front of the robot. The program makes Starting Subset generation Evaluation the Pan-Tilt camera follow the ball. Thus, we can record set θ as the angle of the Pan axis. In the same time we record all the other sensor values. • Secondly, our feature selection algorithms are launched No Stopping off line on the collected data. For a given algorithm, a Criteria subset of relevant sensors is found. • Yes Finally we launch the new Bayesian program and see if Validation the robot can guess the position of the ball, or of another object, without any visual information from its camera. The recognition rate of the position determines the quality Figure 3: General feature selection structure of the sensor selection algorithm. Validation criteria Subset Generation The subset generation stage is a We have different criteria to judge the pertinence of our search procedure in the space of all subsets.
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