May 17th, 2018
(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: firstname.lastname@example.org
To solve a problem like this, you can use MODEL-BASED approaches if you know how likely it is that the robot will move from one state to another (that is, the transition probabilities for each action) or MODEL-FREE approaches (you don’t know how likely it is that the robot will move from state to state, but you can figure out a reward structure).
Markov Decision Process (MDP) – If you know the states, actions, rewards, and transition probabilities (which are probably different for each action), you can determine the optimal policy or “path” through the system, given different starting states. (If transition probabilities have nothing to do with decisions that an agent makes, your MDP reduces to a Markov Chain.)
Reinforcement Learning (RL) – If you know the states, actions, and rewards (but not the transition probabilities), you can still take an unsupervised approach. Just randomly create lots of hops through your system, and use them to update a matrix that describes the average value of each hop within the context of the system.
Solving a RL problem involves finding the optimal value functions (e.g. the Q matrix in Attempt 1) or the optimal policy (the State-Action matrix in Attempt 2). Although there are many techniques for reinforcement learning, we will use Q-learning because we don’t know the transition probabilities for each action. (If we did, we’d model it as a Markov Decision Process and use the MDPtoolbox package instead.) Q-Learning relies on traversing the system in many ways to update a matrix of average expected rewards from each state transition.