Learning Inverse Statics Models Efficiently With Symmetry-Based Exploration

Learning (inverse) kinematics and dynamics models of dexterous robots for the entire action or observation space is challenging and costly. Sampling the entire space is usually intractable in terms of time, tear, and wear. We propose an efficient approach to learn inverse statics models—primarily for gravity compensation—by exploring only a small part of the configuration space and exploiting the symmetry properties of the inverse statics mapping. In particular, there exist symmetric configurations that require the same absolute motor torques to be maintained. We show that those symmetric configurations can be discovered, the functional relations between them can be successfully learned and exploited to generate multiple training samples from one sampled configuration-torque pair. This strategy drastically reduces the number of samples required for learning inverse statics models. Moreover, we demonstrate that exploiting symmetries for learning inverse statics models is a generally applicable strategy for online and offline learning algorithms. We exemplify this by two different learning approaches. First, we modify the Direction Sampling approach for learning inverse statics models online, in a plain exploratory fashion, from scratch and without using a closed-loop controller. Second, we show that inverse statics mappings can be efficiently learned offline utilizing lattice sampling. Results for a 2R planar robot and a 3R simplified human arm demonstrate that their inverse statics mappings can be learned successfully for the entire configuration space. Furthermore, we demonstrate that the number of samples required for learning inverse statics mappings for 2R and 3R manipulators can be reduced at least by factors of approximately 8 and 16, respectively–depending on the number of discovered symmetries

On the criticality of inferred models

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.Comment: 6 pages, 2 figures, version to appear in JSTA

Asset Auctions, Information, and Liquidity

A model is presented of a uniform price auction where bidders compete in demand schedules; the model allows for common and private values in the absence of exogenous noise. It is shown how private information yields more market power than the levels seen with full information. Results obtained here are broadly consistent with evidence from asset auctions, may help explain the response of central banks to the crisis, and suggest potential improvements in the auction formats of asset auctions.adverse selection, market power, reverse auctions, bid shading

A Model of Growth Through Creative Destruction

This paper develops a model based on Schumpeter's process of creative destruction. It departs from existing models of endogenous growth in emphasizing obsolescence of old technologies induced by the accumulation of knowledge and the resulting process or industrial innovations. This has both positive and normative implications for growth. In positive terms, the prospect of a high level of research in the future can deter research today by threatening the fruits of that research with rapid obsolescence. In normative terms, obsolescence creates a negative externality from innovations, and hence a tendency for laissez-faire economies to generate too many innovations, i.e too much growth. This "business-stealing" effect is partly compensated by the fact that innovations tend to be too small under laissez-faire. The model possesses a unique balanced growth equilibrium in which the log of GNP follows a random walk with drift. The size of the drift is the average growth rate of the economy and it is endogenous to the model ; in particular it depends on the size and likelihood of innovations resulting from research and also on the degree of market power available to an innovator.

Human Capital, Financial Innovations and Growth: A Theoretical Approach.

This paper examines the symbiosis between financial development and human capital accumulation in generating endogenous growth. We develop a theoretical model where human capital is a key factor in the creation of financial innovations, resulting in financial development which in turns facilitates the acquisition of new human capital.HUMAN CAPITAL ; ECONOMIC GROWTH ; FINANCIAL ASPECTS

Efficient Jacobian-Based Inverse Kinematics With Sim-to-Real Transfer of Soft Robots by Learning

This paper presents an efficient learning-based method to solve the inverse kinematic (IK) problem on soft robots with highly non-linear deformation. The major challenge of efficiently computing IK for such robots is due to the lack of analytical formulation for either forward or inverse kinematics. To address this challenge, we employ neural networks to learn both the mapping function of forward kinematics and also the Jacobian of this function. As a result, Jacobian-based iteration can be applied to solve the IK problem. A sim-to-real training transfer strategy is conducted to make this approach more practical. We first generate a large number of samples in a simulation environment for learning both the kinematic and the Jacobian networks of a soft robot design. Thereafter, a sim-to-real layer of differentiable neurons is employed to map the results of simulation to the physical hardware, where this sim-to-real layer can be learned from a very limited number of training samples generated on the hardware. The effectiveness of our approach has been verified on pneumatic-driven soft robots for path following and interactive positioning