appliedprobability

ODE method for Stochastic Approximation

We consider the Robbins-Monro update

$x_{n+1} = x_n +\alpha_n [g(x_n) + \epsilon_n]$

and argue that this can be approximated by the o.d.e.:

$\frac{dz}{d t} = g(z(t)).$

Lyapunov functions are an extremely convenient device for proving that a dynamical system converges. We cover:

Here are the slides from Lectures

Please read Section 1.6 from the notes:

Please attempt Ex53, Ex54, Ex56, Ex57.

Here are the slides from Lectures

Please read Section 1.5 from the notes:

Please attempt Ex39, 40 & 41 [if you can code], 42 and 43.

Here are the slides from Lectures

Please read Section 1.4 from the notes:

Please attempt Ex35, Ex36, Ex37.

Here are the slides from Lectures

Please read Section 1.3 from the notes:

Please attempt exercises Ex22, Ex23, Ex24, Ex25.

Here are the slides from Lectures

Please read Section 1.2 from the notes: