Title: Value of Information and Geometry of Optimal Decision-making and Learning

Speaker: Roman V. Belavkin

Abstract:
Mathematical theory of optimal decisions under uncertainty is based on
the idea of maximization of the expected utility functional over a set
of lotteries. This view appears natural for mathematicians, who
consider these lotteries as probability measures on some common
algebra of events, and linear structure of the space of measures leads
to the celebrated in game theory result of von Neumann and Morgenstern
about the existence of a linear or affine objective functional - the
expected utility. Behavioural economists and psychologists, on the
other hand, have demonstrated that people consistently violate the
axioms of expected utility, and this includes professional risk-takers
such as stockbrokers. In this talk I will show how these paradoxes can
be explained if, apart from utility, one also considers the value of
information that a decision-maker receives. This will be a good
opportunity to introduce the value of information theory, which was
developed by Rouslan Stratonovich in the 1960s as an amalgamation of
theories of optimal decision-making and information. I will also
outline a new geometric approach to the value of information, which
will allow us to see that some properties of the optimal value
function are independent of a specific definition of information. We
shall extend this approach to a dynamical system, in which decisions
with information constraints are made sequentially, and define a
frontier corresponding to an optimally learning system. I will show
how this theory gives new insights into parameter control of learning
and optimization algorithms.


There are slides available here:
https://acdl2018.icas.xyz/wp-content/uploads/sites/5/2018/04/Roman-rvb-acdl18-lect2.pdf