# Model Based Reinforcement Learning (MBRL)

Model-based reinforcement learning only differs from its model-free counterpart in learning a *dynamics model*, but that has substantial downstream effects on how the decisions are made.

The dynamics model usually models the environment transition dynamics, \\( s_{t+1} = f_\theta (s_t, a_t) \\), but things like inverse dynamics models (mapping from states to actions) or reward models (predicting rewards) can be used in this framework.

## Simple definition

- There is an agent that repeatedly tries to solve a problem, **accumulating state and action data**.
- With that data, the agent creates a structured learning tool, *a dynamics model*, to reason about the world.
- With the dynamics model, the agent **decides how to act by predicting the future**.
- With those actions, **the agent collects more data, improves said model, and hopefully improves future actions**.

## Academic definition

Model-based reinforcement learning (MBRL) follows the framework of an agent interacting in an environment, **learning a model of said environment**, and then **leveraging the model for control (making decisions).

Specifically, the agent acts in a Markov Decision Process (MDP) governed by a transition function \\( s_{t+1} = f (s_t , a_t) \\) and returns a reward at each step \\( r(s_t, a_t) \\). With a collected dataset \\( D :={ s_i, a_i, s_{i+1}, r_i} \\), the agent learns a model, \\( s_{t+1} = f_\theta (s_t , a_t) \\) **to minimize the negative log-likelihood of the transitions**.

We employ sample-based model-predictive control (MPC) using the learned dynamics model, which optimizes the expected reward over a finite, recursively predicted horizon, \\( \tau \\), from a set of actions sampled from a uniform distribution \\( U(a) \\), (see [paper](https://arxiv.org/pdf/2002.04523) or [paper](https://arxiv.org/pdf/2012.09156.pdf) or [paper](https://arxiv.org/pdf/2009.01221.pdf)).

## Further reading

For more information on MBRL, we recommend you check out the following resources:

- A [blog post on debugging MBRL](https://www.natolambert.com/writing/debugging-mbrl).
- A [recent review paper on MBRL](https://arxiv.org/abs/2006.16712),

## Author

This section was written by  Nathan Lambert 

