Almost Surely T\sqrt{T} Regret Bound for Adaptive LQR

The Linear-Quadratic Regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether $\tilde{ \mathcal{O}}(\sqrt{T})$ regret, which is the best known dependence on time, can be achieved almost surely. In this paper, we propose an adaptive LQR controller with almost surely $\tilde{ \mathcal{O}}(\sqrt{T})$ regret upper bound. The controller features a circuit-breaking mechanism, which circumvents potential safety breach and guarantees the convergence of the system parameter estimate, but is shown to be triggered only finitely often and hence has negligible effect on the asymptotic performance of the controller. The proposed controller is also validated via simulation on Tennessee Eastman Process~(TEP), a commonly used industrial process example

Robot Composite Learning and the Nunchaku Flipping Challenge

Advanced motor skills are essential for robots to physically coexist with humans. Much research on robot dynamics and control has achieved success on hyper robot motor capabilities, but mostly through heavily case-specific engineering. Meanwhile, in terms of robot acquiring skills in a ubiquitous manner, robot learning from human demonstration (LfD) has achieved great progress, but still has limitations handling dynamic skills and compound actions. In this paper, we present a composite learning scheme which goes beyond LfD and integrates robot learning from human definition, demonstration, and evaluation. The method tackles advanced motor skills that require dynamic time-critical maneuver, complex contact control, and handling partly soft partly rigid objects. We also introduce the "nunchaku flipping challenge", an extreme test that puts hard requirements to all these three aspects. Continued from our previous presentations, this paper introduces the latest update of the composite learning scheme and the physical success of the nunchaku flipping challenge

Safe and Efficient Switching Controller Design for Partially Observed Linear-Gaussian Systems

Switching control strategies that unite a potentially high-performance but uncertified controller and a stabilizing albeit conservative controller are shown to be able to balance safety with efficiency, but have been less studied under partial observation of state. To address this gap, we propose a switching control strategy for partially observed linear-Gaussian systems with provable performance guarantees. We show that the proposed switching strategy is both safe and efficient, in the sense that: (1) the linear-quadratic cost of the system is always bounded even if the original uncertified controller is destabilizing; (2) in the case when the uncertified controller is stabilizing, the performance loss induced by the conservativeness of switching converges super-exponentially to zero. The effectiveness of the switching strategy is also demonstrated via numerical simulation on the Tennessee Eastman Process

Fuzzy Random Traveling Salesman Problem

The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Correspondingly, by using the concepts as decision criteria, three fuzzy random programming models for TSP are presented. Finally, a hybrid intelligent algorithm is designed to solve these models, and some numerical examples are provided to illustrate its effectiveness

Distribution of the k-regular partition function modulo composite integers M

Let $b_k(n)$ denote the $k-$regular partitons of a natural number $n$. In this paper, we study the behavior of $b_k(n)$ modulo composite integers $M$ which are coprime to $6$. Specially, we prove that for arbitrary $k-$regular partiton function $b_k(n)$ and integer $M$ coprime to $6$, there are infinitely many Ramanujan-type congruences of $b_k(n)$ modulo $M$

Physics Inspired Optimization on Semantic Transfer Features: An Alternative Method for Room Layout Estimation

In this paper, we propose an alternative method to estimate room layouts of cluttered indoor scenes. This method enjoys the benefits of two novel techniques. The first one is semantic transfer (ST), which is: (1) a formulation to integrate the relationship between scene clutter and room layout into convolutional neural networks; (2) an architecture that can be end-to-end trained; (3) a practical strategy to initialize weights for very deep networks under unbalanced training data distribution. ST allows us to extract highly robust features under various circumstances, and in order to address the computation redundance hidden in these features we develop a principled and efficient inference scheme named physics inspired optimization (PIO). PIO's basic idea is to formulate some phenomena observed in ST features into mechanics concepts. Evaluations on public datasets LSUN and Hedau show that the proposed method is more accurate than state-of-the-art methods.Comment: To appear in CVPR 2017. Project Page: https://sites.google.com/view/st-pio

An improvement on the parity of Schur's partition function

We improve S.-C. Chen's result on the parity of Schur's partition function. Let $A(n)$ be the number of Schur's partitions of $n$, i.e., the number of partitions of $n$ into distinct parts congruent to $1, 2 \mod{3}$. S.-C. Chen \cite{MR3959837} shows $\small \frac{x}{(\log{x})^{\frac{47}{48}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}$. In this paper, we improve Chen's result to $\frac{x}{(\log{x})^{\frac{11}{12}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}.