====== DQN ======

Algorithm 1 Deep Q-learning with Experience Replay

<code>
Initialize replay memory D to capacity N
Initialize action-value function Q with random weights
for episode = 1, M do
Initialise sequence s1 = {x1} and preprocessed sequenced φ1 = φ(s1)
for t = 1, T do
With probability  select a random action at
otherwise select at = maxa Q∗
(φ(st), a; θ)
Execute action at in emulator and observe reward rt and image xt+1
Set st+1 = st, at, xt+1 and preprocess φt+1 = φ(st+1)
Store transition (φt, at, rt, φt+1) in D
Sample random minibatch of transitions (φj , aj , rj , φj+1) from D
Set yj =

rj for terminal φj+1
rj + γ maxa0 Q(φj+1, a0
; θ) for non-terminal φj+1
Perform a gradient descent step on (yj − Q(φj , aj ; θ))2
according to equation 3
end for
end for
</code>