<math>\theta^* = \text{argmax}_\theta E_{\tau \sim p_\theta(\tau)} \left[ \sum_t r(s_t, a_t) \right] </math>. Let's unpack what this means. To phrase it in english, this is basically saying that the optimal policy is one such that the expected value of the total reward over following a trajectory (<math> \tau </math>) determined by the policy is the highest over all policies.

=== Learning Overview ===

Learning involves the agent taking actions # Initialize neural network with input dimensions = observation dimensions and output dimensions = action dimensions. Remember a policy is a mapping from observations to outputs. If the environment returning a new state space is continuous, it may make more sense to make output be one mean and reward. * Input: <math>s_t</math>: States at one standard deviation for each time step* Output: <math>a_t</math>: Actions at each time step* Data: <math>(s_1, a_1, r_1, ..component of the action. , s_T, a_T, r_T)</math>* Learn <math>\pi_\theta # Repeat: s_t -> a_t </math> to maximize <math> \sum_t r_t </math>