Context and scope

In previous lectures…

• saw general OMD & FTRL frameworks for developing online optimization algorithms
• established that $O(\sqrt{T})$ regret is achievable in OCO in a very broad sense

In this lecture:

• general paradigm for obtaining stochastic optimization algorithms from online algorithms
• how good are these stochastic optimization / statistical learning algorithms?
• discuss basic upper and lower bounds in statistical estimation / learning

On the way, we’ll see several important concepts and techniques:

• basics of information theory, the KL-divergence
• information theoretic lower bounds

Recap: Online Mirror Descent (OMD)

Recall the OMD algorithm and its main guarantee, discussed in previous lectures: