Consider a
trader trying to predict whether the stock market will go up or down
each day. Each morning, for T days, he solicits the opinions of n
experts, who each make up/down predictions. Based on their
predictions, the trader makes a choice between up and down, and buys
or sells; accordingly. Suppose that at least one of the experts is
perfect, that is, predicts correctly every day, but the trader
doesn't know which one it is. What should the trader do to minimize
the number of mistakes he makes in T days? This example is just the simplest case of “Adaptive decision making”. For more on this topic, see Chapter 18 in http://homes.cs.washington.edu/~karlin/index.html#Book 
Yuval Peres is the head of the theory group (a group of about
15 researchers who specialize in probability, statistical physics
and algorithms) at Microsoft Research in Redmond, WA. He is
a winner of the Davidson Prize, the Loeve prize and the Robbins
prize, was an ICM speaker in 2002 and was elected as a foreign
member of the National Academy of Sciences in 2016. He is the
author of more than 250 papers and 10 books ranging over
probability theory, ergodic theory, combinatorics and fractals.
