Analytical Solution to a Discrete-Time Model for Dynamic Learning and Decision Making
Management Science · 2022 · Volume 68 · Issue 8
Abstract
Problems concerning dynamic learning and decision making are difficult to solve analytically. We study an infinite-horizon discrete-time model with a constant unknown state that may take two possible values. As a special partially observable Markov decision process (POMDP), this model unifies several types of learning-and-doing problems such as sequential hypothesis testing, dynamic pricing with demand learning, and multiarmed bandits. We adopt a relatively new solution framework from the POMDP literature based on the backward construction of the efficient frontier(s) of continuation-value vectors. This framework accommodates different optimality criteria simultaneously. In the infinite-horizon setting, with the aid of a set of signal quality indices, the extreme points on the efficient frontier can be linked through a set of difference equations and solved analytically. The solution carries structural properties analogous to those obtained under continuous-time models, and it provides a useful tool for making new discoveries through discrete-time models. This paper was accepted by Baris Ata, stochastic models and simulation.
Keywords
learning and doing, sequential hypothesis testing, dynamic pricing with demand learning, multiarmed bandits, partially observable Markov decision processes
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