Deep Q-Network (DQN)
DQN is Q-learning scaled to raw pixels: a deep network approximates Q(s,a) over huge state spaces, and two inventions — an experience replay buffer (shuffled flashcards) and a frozen target network (a slowly-updated answer key) — stop the naive combination from diverging. Double DQN, Dueling, Prioritized Replay, and Rainbow are its landmark refinements.
01.The Problem: Tables Run Out of Squares
Q-learning (topic 201) keeps a table: one row per state, one column per action.
That works beautifully in a grid world. Then you point the agent at a screen.
- Atari has on the order of
10⁶distinct visual states — and that is a generous undercount of what the pixel space can hold. You cannot store a row for each. - Continuous robotics (joint angles, positions, velocities) has infinitely many states. You cannot store those at all.
- Worse: the whole point of deep learning is that similar situations should share knowledge. A table treats "car slightly left of lane" and "car slightly right of lane" as unrelated rows.
What if the Q-table were not a table, but a function?
DQN (Mnih et al., Nature 2015) replaces Q(s,a) with a network Q_θ(s,a) — a CNN that takes the (stacked, preprocessed) screen frames as input and outputs one Q-value per action — and trains it by gradient descent to minimize the TD loss:
L(θ) = E[( y − Q_θ(s,a) )²], with target y = r + γ max_{a'} Q_{θ⁻}(s',a')
Read it as: "squared error against the Bellman-consistent answer" — supervised-learning machinery pointed at the Bellman equation (topic 199) of Q-learning (topic 201).
Naively applying SGD to Q-learning, however, diverges. DQN exists because two specific inventions tame it. That is the story of the rest of this topic.
DQN Architecture & Two Stability Tricks 🧠
DQN Architecture & Two Stability Tricks 🧠
A convolutional network maps stacked frames to a Q-value per action. Two innovations keep deep Q-learning from diverging: (1) an experience replay buffer that decorrelates minibatch updates, and (2) a frozen target network that stabilizes the bootstrapped TD target.
Unlock Topic #202: Deep Q-Network (DQN)
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