Abraar Chaudhry We introduce a family of symmetric convex bodies called generalized ellipsoids of degree \(d\) (GE-\(d\)s), with ellipsoids corresponding to the case of \(d=0\). Generalized ellipsoids (GEs) retain many geometric, algebraic, and algorithmic properties of ellipsoids. We show that the conditions that the parameters of a GE must satisfy can be checked in strongly polynomial time, … Read more
We present generalizations of Newton’s method that incorporate derivatives of an arbitrary order \(d\) but maintain a polynomial dependence on dimension in their cost per iteration. At each step, our \(d^{\text{th}}\)-order method uses semidefinite programming to construct and minimize a sum of squares-convex approximation to the \(d^{\text{th}}\)-order Taylor expansion of the function we wish to … Read more
A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the system … Read more
A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of … Read more