Stochastic analysis [Lecture]

Lecture 18: Stochastic Bandits

Last time we talked about the nonstochatsic bandit problem which was a partial information version of our online learning problem. Here we studied situations where at each iteration t, the learner chooses an action at and suffers loss `t(at) which is the only thing the learner observes. We showed that the importance weighting trick can be plugging into any full information algorithm with a loca...

Lecture Notes on Stochastic Networks

Lecture 21: Stochastic Differential Equations

Following is a quote from [3]. Stochastic differential equations provide a link between probability theory and the much older and more developed fields of ordinary and partial differential equations. Wonderful consequences flow in both directions. The stochastic modeler benefits from centuries of development of the physical sciences, and many classic results of mathematical physics (and even pu...

Lecture Notes: (Stochastic) Optimal Control

2 Stochastic optimal control (discrete time) 2 2.1 The Linear-quadratic-Gaussian (LQG) case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Message passing in LQG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Special case: kinematic control . . . . . . . . . . . . . . . . . . . . . . . . . ...

CSCI - 6971 Lecture Notes : Stochastic processes ∗

Definition 1.1. A stochastic process is a collection of random variables X1,X2, . . . ,Xt parameterized by time. There are a number of aspects of a stochastic process that we can examine. Among them: • dependencies between variables in the sequence • various kinds of long-term averages • the frequency at which “boundary events” occur Some examples of stochastic processes include the following: ...