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7 results (View BibTeX file of all listed publications)

2013

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Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

arxiv link (url) [BibTex]

2013

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L. Learning and Optimization with Submodular Functions ArXiv, May 2013 (techreport)

arxiv link (url) [BibTex]

2009

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The SL simulation and real-time control software package

Schaal, S.

University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

Abstract
SL was originally developed as a Simulation Laboratory software package to allow creating complex rigid-body dynamics simulations with minimal development times. It was meant to complement a real-time robotics setup such that robot programs could first be debugged in simulation before trying them on the actual robot. For this purpose, the motor control setup of SL was copied from our experience with real-time robot setups with vxWorks (Windriver Systems, Inc.)Ñindeed, more than 90% of the code is identical to the actual robot software, as will be explained later in detail. As a result, SL is divided into three software components: 1) the generic code that is shared by the actual robot and the simulation, 2) the robot specific code, and 3) the simulation specific code. The robot specific code is tailored to the robotic environments that we have experienced over the years, in particular towards VME-based multi-processor real-time operating systems. The simulation specific code has all the components for OpenGL graphics simulations and mimics the robot multi-processor environment in simple C-code. Importantly, SL can be used stand-alone for creating graphics an-imationsÑthe heritage from real-time robotics does not restrict the complexity of possible simulations. This technical report describes SL in detail and can serve as a manual for new users of SL.

link (url) [BibTex]

2009

Schaal, S. The SL simulation and real-time control software package University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

link (url) [BibTex]

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The SL simulation and real-time control software package

Schaal, S.

University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

Abstract
SL was originally developed as a Simulation Laboratory software package to allow creating complex rigid-body dynamics simulations with minimal development times. It was meant to complement a real-time robotics setup such that robot programs could first be debugged in simulation before trying them on the actual robot. For this purpose, the motor control setup of SL was copied from our experience with real-time robot setups with vxWorks (Windriver Systems, Inc.)â??indeed, more than 90% of the code is identical to the actual robot software, as will be explained later in detail. As a result, SL is divided into three software components: 1) the generic code that is shared by the actual robot and the simulation, 2) the robot specific code, and 3) the simulation specific code. The robot specific code is tailored to the robotic environments that we have experienced over the years, in particular towards VME-based multi-processor real-time operating systems. The simulation specific code has all the components for OpenGL graphics simulations and mimics the robot multi-processor environment in simple C-code. Importantly, SL can be used stand-alone for creating graphics an-imationsâ??the heritage from real-time robotics does not restrict the complexity of possible simulations. This technical report describes SL in detail and can serve as a manual for new users of SL.

link (url) [BibTex]

Schaal, S. The SL simulation and real-time control software package University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

link (url) [BibTex]

2008

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Efficient inverse kinematics algorithms for highdimensional movement systems

Tevatia, G., Schaal, S.

CLMC Technical Report: TR-CLMC-2008-1, 2008, clmc (techreport)

Abstract
Real-time control of the endeffector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates methods of resolved motion rate control (RMRC) that employ optimization criteria to resolve kinematic redundancies. In particular we focus on two established techniques, the pseudo inverse with explicit optimization and the extended Jacobian method. We prove that the extended Jacobian method includes pseudo-inverse methods as a special solution. In terms of computational complexity, however, pseudo-inverse and extended Jacobian differ significantly in favor of pseudo-inverse methods. Employing numerical estimation techniques, we introduce a computationally efficient version of the extended Jacobian with performance comparable to the original version. Our results are illustrated in simulation studies with a multiple degree-offreedom robot, and were evaluated on an actual 30 degree-of-freedom full-body humanoid robot.

link (url) [BibTex]

2008

Tevatia, G., Schaal, S. Efficient inverse kinematics algorithms for highdimensional movement systems CLMC Technical Report: TR-CLMC-2008-1, 2008, clmc (techreport)

link (url) [BibTex]

2007

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Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract
This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

PDF link (url) [BibTex]

2007

Peters, J. Relative Entropy Policy Search CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

PDF link (url) [BibTex]

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Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract
We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

PDF [BibTex]

Ting, J., Theodorou, E., Schaal, S. Learning an Outlier-Robust Kalman Filter CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

PDF [BibTex]