One-Shot Learning of Manipulation Skills with Online Dynamics Adaptation and Neural Network Priors

One of the key challenges in applying reinforcement learning to complex robotic control tasks is the need to gather large amounts of experience in order to find an effective policy for the task at hand. Model-based reinforcement learning can achieve good sample efficiency, but requires the ability to learn a model of the dynamics that is good enough to learn an effective policy. In this work, we develop a model-based reinforcement learning algorithm that combines prior knowledge from previous tasks with online adaptation of the dynamics model. These two ingredients enable highly sample-efficient learning even in regimes where estimating the true dynamics is very difficult, since the online model adaptation allows the method to locally compensate for unmodeled variation in the dynamics. We encode the prior experience into a neural network dynamics model, adapt it online by progressively refitting a local linear model of the dynamics, and use model predictive control to plan under these dynamics. Our experimental results show that this approach can be used to solve a variety of complex robotic manipulation tasks in just a single attempt, using prior data from other manipulation behaviors

Standard Young Tableaux and Colored Motzkin Paths

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.Comment: 21 page

Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator

The effects of downfolding a Brillouin zone can open gaps and quench the kinetic energy by flattening bands. Quasiperiodic systems are extreme examples of this process, which leads to new phases and critical eigenstates. We analytically and numerically investigate these effects in a two dimensional topological insulator with a quasiperiodic potential and discover a complex phase diagram. We study the nature of the resulting eigenstate quantum phase transitions; a quasiperiodic potential can make a trivial insulator topological and induce topological insulator-to-metal phase transitions through a unique universality class distinct from random systems. This wealth of critical behavior occurs concomitantly with the quenching of the kinetic energy, resulting in flat topological bands that could serve as a platform to realize the fractional quantum Hall effect without a magnetic field.Comment: 6 pages, 4 figures, and supplement materials. Updated results on the flatness ratio, the Berry curvature, and the Chern number of individual band