An Experimental Evaluation of Bayesian Optimization on Bipedal Locomotion

© 2014 IEEE.The design of gaits and corresponding control policies for bipedal walkers is a key challenge in robot locomotion. Even when a viable controller parametrization already exists, finding near-optimal parameters can be daunting. The use of automatic gait optimization methods greatly reduces the need for human expertise and time-consuming design processes. Many different approaches to automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this paper, we present some common methods for automatic gait optimization in bipedal locomotion, and analyze their strengths and weaknesses. We experimentally evaluated these gait optimization methods on a bipedal robot, in more than 1800 experimental evaluations. In particular, we analyzed Bayesian optimization in different configurations, including various acquisition functions

Learning Deep Belief Networks from Non-Stationary Streams

Deep learning has proven to be beneficial for complex tasks such as classifying images. However, this approach has been mostly applied to static datasets. The analysis of non-stationary (e.g., concept drift) streams of data involves specific issues connected with the temporal and changing nature of the data. In this paper, we propose a proof-of-concept method, called Adaptive Deep Belief Networks, of how deep learning can be generalized to learn online from changing streams of data. We do so by exploiting the generative properties of the model to incrementally re-train the Deep Belief Network whenever new data are collected. This approach eliminates the need to store past observations and, therefore, requires only constant memory consumption. Hence, our approach can be valuable for life-long learning from non-stationary data streams. © 2012 Springer-Verlag

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbour Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a plasmon-like mode which, for wavevectors close to (pi,pi), increases in amplitude and softens as the charge ordering transition is approached. We propose that inelastic X-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with dxy symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge ordering transition.Comment: 22 pages, 16 eps figures; caption of Fig. 5 correcte

Bayesian Gait Optimization for Bipedal Locomotion

One of the key challenges in robotic bipedal locomotion is finding gait parameters that optimize a desired performance criterion, such as speed, robustness or energy efficiency. Typically, gait optimization requires extensive robot experiments and specific expert knowledge. We propose to apply data-driven machine learning to automate and speed up the process of gait optimization. In particular, we use Bayesian optimization to efficiently find gait parameters that optimize the desired performance metric. As a proof of concept we demonstrate that Bayesian optimization is near-optimal in a classical stochastic optimal control framework. Moreover, we validate our approach to Bayesian gait optimization on a low-cost and fragile real bipedal walker and show that good walking gaits can be efficiently found by Bayesian optimization. © 2014 Springer International Publishing

Effect of dimensionality on the charge-density-wave in few-layers 2H-NbSe2_2

We investigate the charge density wave (CDW) instability in single and double layers, as well as in the bulk 2H-NbSe$_{2}$. We demonstrate that the density functional theory correctly describes the metallic CDW state in the bulk 2H-NbSe$_{2}$. We predict that both mono- and bilayer NbSe$_{2}$ undergo a CDW instability. However, while in the bulk the instability occurs at a momentum $\mathbf{q}_{CDW}\approx{2/3}\mathbf{\Gamma M}$, in free-standing layers it occurs at $\mathbf{q}_{CDW}\approx{1/2}\mathbf{\Gamma M}$. Furthermore, while in the bulk the CDW leads to a metallic state, in a monolayer the ground state becomes semimetallic, in agreement with recent experimental data. We elucidate the key role that an enhancement of the electron-phonon matrix element at $\mathbf{q}\approx\mathbf{q}_{CDW}$ plays in forming the CDW ground state.Comment: 4 pages 5 figure

Bayesian Optimization for Learning Gaits under Uncertainty

© 2015, Springer International Publishing Switzerland.Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal parameters can be daunting. Typically, this kind of parameter optimization requires specific expert knowledge and extensive robot experiments. Automatic black-box gait optimization methods greatly reduce the need for human expertise and time-consuming design processes. Many different approaches for automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this article, we thoroughly discuss multiple automatic optimization methods in the context of gait optimization. We extensively evaluate Bayesian optimization, a model-based approach to black-box optimization under uncertainty, on both simulated problems and real robots. This evaluation demonstrates that Bayesian optimization is particularly suited for robotic applications, where it is crucial to find a good set of gait parameters in a small number of experiments

Adiabatic and non-adiabatic phonon dispersion in a Wannier function approach

We develop a first-principles scheme to calculate adiabatic and non-adiabatic phonon frequencies in the full Brillouin zone. The method relies on the variational properties of a force-constants functional with respect to the first-order perturbation of the electronic charge density and on the localization of the deformation potential in the Wannier function basis. This allows for calculation of phonon dispersion curves free from convergence issues related to Brillouin zone sampling. In addition our approach justify the use of the static screened potential in the calculation of the phonon linewidth due to decay in electron-hole pairs. We apply the method to the calculation of the phonon dispersion and electron-phonon coupling in MgB$_2$ and CaC$_6$. In both compounds we demonstrate the occurrence of several Kohn anomalies, absent in previous calculations, that are manifest only after careful electron and phonon momentum integration. In MgB$_2$, the presence of Kohn anomalies on the E$_{2g}$ branches improves the agreement with measured phonon spectra and affects the position of the main peak in the Eliashberg function. In CaC$_6$ we show that the non-adiabatic effects on in-plane carbon vibrations are not localized at zone center but are sizable throughout the full Brillouin zone. Our method opens new perspectives in large-scale first-principles calculations of dynamical properties and electron-phonon interaction.Comment: 18 pages, 8 figure

Thermodynamic stabilities of ternary metal borides: An ab initio guide for synthesizing layered superconductors

Density functional theory calculations have been used to identify stable layered Li-$M$-B crystal structure phases derived from a recently proposed binary metal-sandwich (MS) lithium monoboride superconductor. We show that the MS lithium monoboride gains in stability when alloyed with electron-rich metal diborides; the resulting ordered Li$_{2(1-x)}M_x$B$_2$ ternary phases may form under normal synthesis conditions in a wide concentration range of $x$ for a number of group-III-V metals $M$. In an effort to pre-select compounds with the strongest electron-phonon coupling we examine the softening of the in-plane boron phonon mode at $\Gamma$ in a large class of metal borides. Our results reveal interesting general trends for the frequency of the in-plane boron phonon modes as a function of the boron-boron bond length and the valence of the metal. One of the candidates with a promise to be an MgB$_2$-type superconductor, Li$_2$AlB$_4$, has been examined in more detail: according to our {\it ab initio} calculations of the phonon dispersion and the electron-phonon coupling $\lambda$, the compound should have a critical temperature of $\sim4$ K.Comment: 10 pages, 9 figures, submitted to PR

A modified discontinuous Galerkin method for solving efficiently Helmholtz problems

A new solution methodology is proposed for solving efficiently Helmholtz problems. The proposed method falls in the category of the discontinuous Galerkin methods. However, unlike the existing solution methodologies, this method requires solving (a) well-posed local problems to determine the primal variable, and (b) a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges. Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology