Online portfolio selection is a fundamental problem in computational finance, which has
been extensively studied across several research communities, including finance, statistics …

In this monograph, I introduce the basic concepts of Online Learning through a modern view
of Online Convex Optimization. Here, online learning refers to the framework of regret …

We show that parametric models trained by a stochastic gradient method (SGM) with few
iterations have vanishing generalization error. We prove our results by arguing that SGM is …

This monograph portrays optimization as a process. In many practical applications the
environment is so complex that it is infeasible to lay out a comprehensive theoretical model …

In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning),
a method for trajectory optimization invariant to reparametrization. CHOMP uses functional …

Sequential prediction problems such as imitation learning, where future observations
depend on previous predictions (actions), violate the common iid assumptions made in …

We present a new family of subgradient methods that dynamically incorporate knowledge of
the geometry of the data observed in earlier iterations to perform more informative gradient …

We study two communication-efficient algorithms for distributed statistical optimization on
large-scale data. The first algorithm is an averaging method that distributes the $ N $ data …

Existing high-dimensional motion planning algorithms are simultaneously overpowered and
underpowered. In domains sparsely populated by obstacles, the heuristics used by …

We describe and analyze a simple and effective iterative algorithm for solving the
optimization problem cast by Support Vector Machines (SVM). Our method alternates …