Martin Biehl

ビエール・マーティン

Cross Labs, Cross Compass

When can we see a Moore machine as an agent?

Saturday, April 6th, 10:30–11:00

Under what circumstances can we legitimately claim that a system with inputs and outputs, is an agent? Informally, a fair answer would be that we can claim this if we can show that the system a) has beliefs about an environment model causing its inputs, b) a goal within that environment model, and c) acts optimally according to its belief in order to achieve a goal. Our recent work formalizes this answer for a specific class of systems with inputs and outputs called Moore machines. 

For this we employ mostly notions familiar from the literature on partially observable Markov decision problems (POMDPs). Specifically, we consider environment models as stochastic Mealy machines (including hidden state) that take output from the Moore machine and in response produce inputs and rewards. Beliefs are represented by probability distributions over the hidden states, and goals are formally the maximization of expected rewards. 

The main additional ingredient is the interpretation map or belief map which is a function from the internal state of the Moore machine to the set of probability distributions over the hidden state of the environment model that obeys a consistency condition. Belief maps allow us to formalize what it means that a Moore machine “has beliefs about the environment model”. This is due to the consistency condition which ensures that the internal state dynamics of the Moore machine implement Bayesian updating of the beliefs they are mapped to by the belief map. 

So if we find, for a given Moore machine, an environment model and an according (consistent) belief map this shows it has beliefs about this model. To justify that we can see this Moore machine as an agent it then remains to check whether the output of the Moore machine in a given state is equal to the optimal action for the belief associated to that state.

The result is that we have a formal sufficient condition for when a Moore machine can be interpreted as an agent. We believe that this is only a special case and that the approach can be extended beyond Moore machines and the POMDP inspired case.

In this talk I will present the details of this approach and comment on some consequences such as the separation of the notion of agency from that of capability or power.