A friend and I were looking at the following diagram the other day of a multi-objective Q value network.

Image Credit: Runzhe Yang

And my friend, asked: “Why can’t the weight preferences be considered part of the state?” The network takes both state and weights as input, so why not just consider weighs as part of the state, which can be formulated however we want?

I had to go back to the formal definition of a Markov Decision Process.

In an MDP is a 4-tuple (S, A, P, R), where P is the probability of the next state given a current state and action.

Weight preferences, however, are not part of this equation. Weight preferences typically come from the a user, and in multi-objective reinforcement learning, the problem setting deals with not knowing a user’s weight preferences beforehand.