Reinforcement Learning Methods for Wordle: A POMDP/Adaptive Control Approach

In this paper, we discuss a Reinforcement Learning (RL) approach towards a class of sequential decision problems, exemplified for the popular Wordle puzzle that appears daily in the New York Times. Wordle involves a list of 5-letter mystery words, which is a subset of a larger list of guess words. A word is selected at random from the mystery list, and the objective is to find that word by sequentially selecting no more than six words from the guess list. Each guess word selection provides information about the letters contained in the hidden mystery word according to a given set of rules, which involves color coding of letters shared by the guess word and the mystery word. We will adopt a more general point of view, by considering a broad class of problems that include Wordle as a special case. In particular, the problems that we consider include sequential search situations, where the objective is to guess correctly an unknown object from a given finite set of objects (the set of mystery words in the Wordle context), by using a sequence of decisions from a finite set (the set of guess words in Wordle), which result in a sequence of corresponding observations (the information outcomes of the guesses in Wordle). We aim to minimize some cost function, such as the expected number of observations required to determine the unknown object. Within the search context just described, some basic information theory concepts are relevant, which have already been applied to Wordle, and are important for our methodology.