# Are linear approximators better suited to some tasks compared to complex neural net functions?

Model based RL attempts to learn a function $$f(s_{t+1}|s_t, a_t)$$ representing the environment transitions, otherwise known as a model of the system. I see linear functions are still being used in model-based RL such as in robotic manipulation to learn system dynamics, and can work effectively well. (Here, I mean in learning the model, not as an optimization method for the controller selecting the best actions).

In model-based RL, are there situations where a learning a linear model such as using a Lyapunov function would be better suited than using a neural network, or are the examples of problems framed to use linear models when addressing them using model-based RL?

• This might be helpful: "Linear approximations of non-linear physical systems prove accurate and are well accepted in many fields. For the comprehensive study, see Linear models of nonlinear systems" Sep 26 '20 at 6:28

This is just a case of supervised learning. You are trying to predict $$s_{t+1}$$ given $$s_t$$ and $$a_t$$, so the answer to your question depends on how complex your state dynamics are.
• Yes, state space will be key. This work uses a $32 * 32$ image on a linear model. Would that be termed as complex? Sep 14 '20 at 15:14