Task-Driven Estimation and Control via Information Bottlenecks

Our goal is to develop a principled and general algorithmic framework for task-driven estimation and control for robotic systems. State-of-the-art approaches for controlling robotic systems typically rely heavily on accurately estimating the full state of the robot (e.g., a running robot might estimate joint angles and velocities, torso state, and position relative to a goal). However, full state representations are often excessively rich for the specific task at hand and can lead to significant computational inefficiency and brittleness to errors in state estimation. In contrast, we present an approach that eschews such rich representations and seeks to create task-driven representations. The key technical insight is to leverage the theory of information bottlenecks}to formalize the notion of a "task-driven representation" in terms of information theoretic quantities that measure the minimality of a representation. We propose novel iterative algorithms for automatically synthesizing (offline) a task-driven representation (given in terms of a set of task-relevant variables (TRVs)) and a performant control policy that is a function of the TRVs. We present online algorithms for estimating the TRVs in order to apply the control policy. We demonstrate that our approach results in significant robustness to unmodeled measurement uncertainty both theoretically and via thorough simulation experiments including a spring-loaded inverted pendulum running to a goal location.Comment: 9 pages, 4 figures, abridged version accepted to ICRA2019; Incorporates changes in final conference submissio

On characterization of a class of convex operators for pricing insurance risks

The properties of risk measures or insurance premium principles have been extensively studied in actuarial literature. We propose an axiomatic description of a particular class of coherent risk measures defined in Artzner, Delbaen, Eber, and Heath (1999). The considered risk measures are obtained by expansion of TVar measures, consequently they look like very interesting in insurance pricing where TVar measures is frequently used to value tail risks.Risk measures, premium principles,Choquet measures distortion function,TVar .

Eigenvalue Estimates for submanifolds of N×RN \times \mathbb{R} with locally bounded mean curvature

We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in $N \times \mathbb{R}$, where $N$ is an $n$-dimensional complete Riemannian manifold with radial sectional curvature $K_{N} \leq \kappa$. When the immersion is minimal our estimates are sharp. We also show that cylindrically bounded minimal surfaces has positive fundamental tone.Comment: 9 page

On the characterization of convex premium principles

In actuarial literature the properties of risk measures or insurance premium principles have been extensively studied . We propose a characterization of a particular class of coherent risk measures defined in [1]. The considered premium principles are obtained by expansion of TVar measures, consequently they look like very interesting in insurance pricing where TVar measures is frequently used to value tail risks.risk measures, premium principles, capacity, distortion function, TVar