Playing Atari with Deep Reinforcement Learning

Volodymyr Mnih

Koray Kavukcuoglu

David Silver

Daan Wierstra

Alex Graves

Ioannis Antonoglou

Martin Riedmiller

DeepMind Technologies{vlad,koray,david,alex.graves,ioannis,daan,martin.riedmiller} @ deepmind.com

Abstract
We present the first deep learning model to successfully learn control policies directly from high-dimensional sensory input using reinforcement learning. The
model is a convolutional neural network, trained with a variant of Q-learning,whose input is raw pixels and whose output is a value function estimating future
rewards. We apply our method to seven Atari 2600 games from the Arcade Learning Environment, with no adjustment of the architecture or learning algorithm. We
find that it outperforms all previous approaches on six of the games and surpasses
a human expert on three of them.

1

Introduction

Learning to control agents directly from high-dimensional sensory inputs like vision and speech isone of the long-standing challenges of reinforcement learning (RL). Most successful RL applications that operate on these domains have relied on hand-crafted features combined with linear valuefunctions or policy representations. Clearly, the performance of such systems heavily relies on thequality of the feature representation.
Recent advances in deep learning have made it possible to extract high-level features from raw sensory data, leading to breakthroughs in computer vision [11, 22, 16] and speech recognition [6, 7].
These methods utilise a range of neural network architectures, including convolutional networks,
multilayer perceptrons, restricted Boltzmann machines and recurrent neural networks, and have exploited both supervised and unsupervised learning. It seems natural to ask whether similar techniques could also be beneficial for RL with sensory data.
However reinforcement learning presents several challenges from a deep learning perspective.
Firstly, most successful deep learning applications to date have required large amounts of handlabelled training data. RL algorithms, on the other hand, must be able to learn from a scalar reward
signal that is frequently sparse, noisy and delayed. The delay between actions and resulting rewards,
which can be thousands of timesteps long, seems particularly daunting when compared to the direct
association between inputs and targets found in supervised learning. Another issue is that most deeplearning algorithms assume the data samples to be independent, while in reinforcement learning one
typically encounters sequences of highly correlated states. Furthermore, in RL the data distribution changes as the algorithm learns new behaviours, which can be problematic for deep learning
methods that assume a fixed underlying distribution.
This paper demonstrates that a convolutional neural network can overcome these challenges to learn
successful control policies from raw video data in complex RL environments. The network is
trained with a variant of the Q-learning [26] algorithm, with stochastic gradient descent to update
the weights. To alleviate the problems of correlated data and non-stationary distributions, we use
1

Figure 1: Screen shots from five Atari 2600 Games: (Left-to-right) Pong, Breakout, Space Invaders,
Seaquest, Beam Rider

an experience replay mechanism [13] which randomly samples previous transitions, and therebysmooths the training distribution over many past behaviors.
We apply our approach to a range of Atari 2600 games implemented in The Arcade Learning Environment (ALE) [3]. Atari 2600 is a challenging RL testbed that presents agents with a high dimensional visual input (210 × 160 RGB video at 60Hz) and a diverse and interesting set of tasks thatwere designed to be difficult for humans players. Our goal is to create a single neural network agent
that is able to successfully learn to play as many of the games as possible. The network was not provided with any game-specific information or hand-designed visual features, and was not privy to theinternal state of the emulator; it learned from nothing but the video input, the reward and terminal
signals, and the set of possible actions—just as a human player would. Furthermore the network architecture and all hyperparameters used for training were kept constant across the games. So far the
network has outperformed all previous RL algorithms on six of the seven games we have attemptedand surpassed an expert human player on three of them. Figure 1 provides sample screenshots fromfive of the games used for training.

2

BackgroundWe consider tasks in which an agent interacts with an environment E, in this case the Atari emulator,
in a sequence of actions, observations and rewards. At each time-step the agent selects an action
at from the set of legal game actions, A = {1, . . . , K}. The action is passed to the emulator andmodifies its internal state and the game score. In general E may be stochastic. The emulator’sinternal state is not observed by the agent; instead it observes an image xt ∈ Rd from the emulator,
which is a vector of raw pixel values representing the current screen. In addition it receives a reward
rt representing the change in game score. Note that in general the game score may depend on thewhole prior sequence of actions and observations; feedback about an action may only be received
after many thousands of time-steps have elapsed.
Since the agent only observes images of the current screen, the task is partially observed and manyemulator states are perceptually aliased, i.e. it is impossible to fully understand the current situationfrom only the current screen xt . We therefore consider sequences of actions and observations, st =x1 , a1 , x2 , ..., at−1 , xt , and learn game strategies that depend upon these sequences. All sequencesin the emulator are assumed to terminate in a finite number of time-steps. This formalism gives
rise to a large but finite Markov decision process (MDP) in which each sequence is a distinct state.
As a result, we can apply standard reinforcement learning methods for MDPs, simply by using thecomplete sequence st as the state representation at time t.
The goal of the agent is to interact with the emulator by selecting actions in a way that maximises
future rewards. We make the standard assumption that future rewards are discounted by a factor ofPT0γ per time-step, and define the future discounted return at time t as Rt = t0 =t γ t −t rt0 , where T
is the time-step at which the game terminates. We define the optimal action-value function Q∗ (s, a)as the maximum expected return achievable by following any strategy, after seeing some sequences and then taking some action a, Q∗ (s, a) = maxπ E [Rt |st = s, at = a, π], where π is a policy
mapping sequences to actions (or distributions over actions).
The optimal action-value function obeys an important identity known as the Bellman equation. Thisis based on the following intuition: if the optimal value Q∗ (s0 , a0 ) of the sequence s0 at the nexttime-step was known for all possible actions a0 , then the optimal strategy is to select the action a0
2

maximising the expected value of r + γQ∗ (s0 , a0 ),
i
h
∗ 0 0
s,
a
Q∗ (s, a) = Es0 ∼E r + γ max
Q
(s
,
a
)
0
a

(1)

The basic idea behind many reinforcement learning algorithms is to estimate the actionvalue function, by using the Bellman equation as an iterative update, Qi+1 (s, a) =E [r + γ maxa0 Qi (s0 , a0 )|s, a]. Such value iteration algorithms converge to the optimal actionvalue function, Qi → Q∗ as i → ∞ [23]. In practice, this basic approach is totally impractical,
because the action-value function is estimated separately for each sequence, without any generalisation. Instead, it is common to use a function approximator to estimate the action-value function,
Q(s, a; θ) ≈ Q∗ (s, a). In the reinforcement learning community this is typically a linear function
approximator, but sometimes a non-linear function approximator is used instead, such as a neuralnetwork. We refer to a neural network function approximator with weights θ as a Q-network. A
Q-network can be trained by minimising a sequence of loss functions Li (θi ) that changes at each
iteration i,hi2
Li (θi ) = Es,a∼ρ(·) (yi − Q (s, a; θi )) ,(2)
where yi = Es0 ∼E [r + γ maxa0 Q(s0 , a0 ; θi−1 )|s, a] is the target for iteration i and ρ(s, a) is a
probability distribution over sequences s and actions a that we refer to as the behaviour distribution.
The parameters from the previous iteration θi−1 are held fixed when optimising the loss function
Li (θi ). Note that the targets depend on the network weights; this is in contrast with the targets used
for supervised learning, which are fixed before learning begins. Differentiating the loss function
with respect to the weights we arrive at the following gradient,
h

i
0 0
∇θi Li (θi ) = Es,a∼ρ(·);s0 ∼E r + γ max
Q(s
,
a
;
θ
)
−
Q(s,
a;
θ
)
∇
Q(s,
a;
θ
)
. (3)
i−1
i
θ
i
i
0
a

Rather than computing the full expectations in the above gradient, it is often computationally expedient to optimise the loss function by stochastic gradient descent. If the weights are updated after
every time-step, and the expectations are replaced by single samples from the behaviour distribution
ρ and the emulator E respectively, then we arrive at the familiar Q-learning algorithm [26].
Note that this algorithm is model-free: it solves the reinforcement learning task directly using samples from the emulator E, without explicitly constructing an estimate of E. It is also off-policy: itlearns about the greedy strategy a = maxa Q(s, a; θ), while following a behaviour distribution that
ensures adequate exploration of the state space. In practice, the behaviour distribution is often selected by an -greedy strategy that follows the greedy strategy with probability 1 −  and selects a
random action with probability .

3Related Work

Perhaps the best-known success story of reinforcement learning is TD-gammon, a backgammonplaying program which learnt entirely by reinforcement learning and self-play, and achieved a superhuman level of play [24]. TD-gammon used a model-free reinforcement learning algorithm similar
to Q-learning, and approximated the value function using a multi-layer perceptron with one hidden
layer1 .
However, early attempts to follow up on TD-gammon, including applications of the same method tochess, Go and checkers were less successful. This led to a widespread belief that the TD-gammon
approach was a special case that only worked in backgammon, perhaps because the stochasticity inthe dice rolls helps explore the state space and also makes the value function particularly smooth[19].
Furthermore, it was shown that combining model-free reinforcement learning algorithms such as Qlearning with non-linear function approximators [25], or indeed with off-policy learning [1] could
cause the Q-network to diverge. Subsequently, the majority of work in reinforcement learning focused on linear function approximators with better convergence guarantees [25].
1
In fact TD-Gammon approximated the state value function V (s) rather than the action-value function
Q(s, a), and learnt on-policy directly from the self-play games3

More recently, there has been a revival of interest in combining deep learning with reinforcement
learning. Deep neural networks have been used to estimate the environment E; restricted Boltzmann
machines have been used to estimate the value function [21]; or the policy [9]. In addition, thedivergence issues with Q-learning have been partially addressed by gradient temporal-difference
methods. These methods are proven to converge when evaluating a fixed policy with a nonlinear
function approximator [14]; or when learning a control policy with linear function approximation
using a restricted variant of Q-learning [15]. However, these methods have not yet been extended tononlinear control.
Perhaps the most similar prior work to our own approach is neural fitted Q-learning (NFQ) [20].
NFQ optimises the sequence of loss functions in Equation 2, using the RPROP algorithm to update
the parameters of the Q-network. However, it uses a batch update that has a computational cost
per iteration that is proportional to the size of the data set, whereas we consider stochastic gradient
updates that have a low constant cost per iteration and scale to large data-sets. NFQ has also beensuccessfully applied to simple real-world control tasks using purely visual input, by first using deep
autoencoders to learn a low dimensional representation of the task, and then applying NFQ to thisrepresentation [12]. In contrast our approach applies reinforcement learning end-to-end, directlyfrom the visual inputs; as a result it may learn features that are directly relevant to discriminating
action-values. Q-learning has also previously been combined with experience replay and a simple
neural network [13], but again starting with a low-dimensional state rather than raw visual inputs.
The use of the Atari 2600 emulator as a reinforcement learning platform was introduced by [3], whoapplied standard reinforcement learning algorithms with linear function approximation and genericvisual features. Subsequently, results were improved by using a larger number of features, andusing tug-of-war hashing to randomly project the features into a lower-dimensional space [2]. The
HyperNEAT evolutionary architecture [8] has also been applied to the Atari platform, where it wasused to evolve (separately, for each distinct game) a neural network representing a strategy for thatgame. When trained repeatedly against deterministic sequences using the emulator’s reset facility,
these strategies were able to exploit design flaws in several Atari games.

4

Deep Reinforcement Learning

Recent breakthroughs in computer vision and speech recognition have relied on efficiently training
deep neural networks on very large training sets. The most successful approaches are trained directlyfrom the raw inputs, using lightweight updates based on stochastic gradient descent. By feeding
sufficient data into deep neural networks, it is often possible to learn better representations than
handcrafted features [11]. These successes motivate our approach to reinforcement learning. Our
goal is to connect a reinforcement learning algorithm to a deep neural network which operates
directly on RGB images and efficiently process training data by using stochastic gradient updates.
Tesauro’s TD-Gammon architecture provides a starting point for such an approach. This architecture updates the parameters of a network that estimates the value function, directly from on-policy
samples of experience, st , at , rt , st+1 , at+1 , drawn from the algorithm’s interactions with the environment (or by self-play, in the case of backgammon). Since this approach was able to outperformthe best human backgammon players 20 years ago, it is natural to wonder whether two decades of
hardware improvements, coupled with modern deep neural network architectures and scalable RL
algorithms might produce significant progress.
In contrast to TD-Gammon and similar online approaches, we utilize a technique known as experience replay [13] where we store the agent’s experiences at each time-step, et = (st , at , rt , st+1 )in a data-set D = e1 , ..., eN , pooled over many episodes into a replay memory. During the inner
loop of the algorithm, we apply Q-learning updates, or minibatch updates, to samples of experience,e ∼ D, drawn at random from the pool of stored samples. After performing experience replay,
the agent selects and executes an action according to an -greedy policy. Since using histories ofarbitrary length as inputs to a neural network can be difficult, our Q-function instead works on fixed
length representation of histories produced by a function φ. The full algorithm, which we call deep
Q-learning, is presented in Algorithm 1.
This approach has several advantages over standard online Q-learning [23]. First, each step ofexperience is potentially used in many weight updates, which allows for greater data efficiency.
4

Algorithm 1 Deep Q-learning with Experience Replay
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 atotherwise 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rj
for terminal φj+1
Set yj =rj + γ maxa0 Q(φj+1 , a0 ; θ)for non-terminal φj+1
2
Perform a gradient descent step on (yj − Q(φj , aj ; θ)) according to equation 3
end forend for

Second, learning directly from consecutive samples is inefficient, due to the strong correlations
between the samples; randomizing the samples breaks these correlations and therefore reduces thevariance of the updates. Third, when learning on-policy the current parameters determine the next
data sample that the parameters are trained on. For example, if the maximizing action is to move leftthen the training samples will be dominated by samples from the left-hand side; if the maximizing
action then switches to the right then the training distribution will also switch. It is easy to see how
unwanted feedback loops may arise and the parameters could get stuck in a poor local minimum, oreven diverge catastrophically [25]. By using experience replay the behavior distribution is averaged
over many of its previous states, smoothing out learning and avoiding oscillations or divergence inthe parameters. Note that when learning by experience replay, it is necessary to learn off-policy(because our current parameters are different to those used to generate the sample), which motivatesthe choice of Q-learning.
In practice, our algorithm only stores the last N experience tuples in the replay memory, and samples
uniformly at random from D when performing updates. This approach is in some respects limited
since the memory buffer does not differentiate important transitions and always overwrites withrecent transitions due to the finite memory size N . Similarly, the uniform sampling gives equal
importance to all transitions in the replay memory. A more sophisticated sampling strategy mightemphasize transitions from which we can learn the most, similar to prioritized sweeping [17].
4.1Preprocessing and Model Architecture

Working directly with raw Atari frames, which are 210 × 160 pixel images with a 128 color palette,
can be computationally demanding, so we apply a basic preprocessing step aimed at reducing the
input dimensionality. The raw frames are preprocessed by first converting their RGB representation
to gray-scale and down-sampling it to a 110×84 image. The final input representation is obtained bycropping an 84 × 84 region of the image that roughly captures the playing area. The final cropping
stage is only required because we use the GPU implementation of 2D convolutions from [11], which
expects square inputs. For the experiments in this paper, the function φ from algorithm 1 applies thispreprocessing to the last 4 frames of a history and stacks them to produce the input to the Q-function.
There are several possible ways of parameterizing Q using a neural network. Since Q maps historyaction pairs to scalar estimates of their Q-value, the history and the action have been used as inputs
to the neural network by some previous approaches [20, 12]. The main drawback of this typeof architecture is that a separate forward pass is required to compute the Q-value of each action,
resulting in a cost that scales linearly with the number of actions. We instead use an architecturein which there is a separate output unit for each possible action, and only the state representation isan input to the neural network. The outputs correspond to the predicted Q-values of the individual
action for the input state. The main advantage of this type of architecture is the ability to compute
Q-values for all possible actions in a given state with only a single forward pass through the network.
5

We now describe the exact architecture used for all seven Atari games. The input to the neuralnetwork consists is an 84 × 84 × 4 image produced by φ. The first hidden layer convolves 16 8 × 8
filters with stride 4 with the input image and applies a rectifier nonlinearity [10, 18]. The second
hidden layer convolves 32 4 × 4 filters with stride 2, again followed by a rectifier nonlinearity. The
final hidden layer is fully-connected and consists of 256 rectifier units. The output layer is a fullyconnected linear layer with a single output for each valid action. The number of valid actions varied
between 4 and 18 on the games we considered. We refer to convolutional networks trained with ourapproach as Deep Q-Networks (DQN).

5Experiments

So far, we have performed experiments on seven popular ATARI games – Beam Rider, Breakout,
Enduro, Pong, Q*bert, Seaquest, Space Invaders. We use the same network architecture, learningalgorithm and hyperparameters settings across all seven games, showing that our approach is robust
enough to work on a variety of games without incorporating game-specific information. While weevaluated our agents on the real and unmodified games, we made one change to the reward structureof the games during training only. Since the scale of scores varies greatly from game to game, we
fixed all positive rewards to be 1 and all negative rewards to be −1, leaving 0 rewards unchanged.
Clipping the rewards in this manner limits the scale of the error derivatives and makes it easier to
use the same learning rate across multiple games. At the same time, it could affect the performanceof our agent since it cannot differentiate between rewards of different magnitude.
In these experiments, we used the RMSProp algorithm with minibatches of size 32. The behavior
policy during training was -greedy with  annealed linearly from 1 to 0.1 over the first million
frames, and fixed at 0.1 thereafter. We trained for a total of 10 million frames and used a replay
memory of one million most recent frames.
Following previous approaches to playing Atari games, we also use a simple frame-skipping technique [3]. More precisely, the agent sees and selects actions on every k th frame instead of every
frame, and its last action is repeated on skipped frames. Since running the emulator forward for one
step requires much less computation than having the agent select an action, this technique allows
the agent to play roughly k times more games without significantly increasing the runtime. We use
k = 4 for all games except Space Invaders where we noticed that using k = 4 makes the lasers
invisible because of the period at which they blink. We used k = 3 to make the lasers visible andthis change was the only difference in hyperparameter values between any of the games.
5.1

Training and Stability

In supervised learning, one can easily track the performance of a model during training by evaluating
it on the training and validation sets. In reinforcement learning, however, accurately evaluating the
progress of an agent during training can be challenging. Since our evaluation metric, as suggested
by [3], is the total reward the agent collects in an episode or game averaged over a number ofgames, we periodically compute it during training. The average total reward metric tends to be very
noisy because small changes to the weights of a policy can lead to large changes in the distribution ofstates the policy visits . The leftmost two plots in figure 2 show how the average total reward evolves
during training on the games Seaquest and Breakout. Both averaged reward plots are indeed quite
noisy, giving one the impression that the learning algorithm is not making steady progress. Another,more stable, metric is the policy’s estimated action-value function Q, which provides an estimate of
how much discounted reward the agent can obtain by following its policy from any given state. We
collect a fixed set of states by running a random policy before training starts and track the averageof the maximum2 predicted Q for these states. The two rightmost plots in figure 2 show that average
predicted Q increases much more smoothly than the average total reward obtained by the agent andplotting the same metrics on the other five games produces similarly smooth curves. In addition
to seeing relatively smooth improvement to predicted Q during training we did not experience any
divergence issues in any of our experiments. This suggests that, despite lacking any theoreticalconvergence guarantees, our method is able to train large neural networks using a reinforcement
learning signal and stochastic gradient descent in a stable manner.
2

The maximum for each state is taken over the possible actions.

6

100
50
0

0

10 20 30 40 50 60 70 80 90 100
Training Epochs

0

Average Q on Breakout

4

10 20 30 40 50 60 70 80 90 100
Training Epochs

Average Action Value (Q)150

Average Reward on Seaquest
Average Action Value (Q)

200

1800
1600
1400
1200
1000
800
600
400
200
0

Average Reward per EpisodeAverage Reward per EpisodeAverage Reward on Breakout

250

3.5
3
2.5
2
1.5
1
0.5
0

0

10 20 30 40 50 60 70 80 90 100
Training Epochs

9
8
7
6
5
4
3
2
1
0

Average Q on Seaquest

0

10 20 30 40 50 60 70 80 90 100
Training Epochs

Figure 2: The two plots on the left show average reward per episode on Breakout and Seaquest
respectively during training. The statistics were computed by running an -greedy policy with  =0.05 for 10000 steps. The two plots on the right show the average maximum predicted action-valueof a held out set of states on Breakout and Seaquest respectively. One epoch corresponds to 50000
minibatch weight updates or roughly 30 minutes of training time.

Figure 3: The leftmost plot shows the predicted value function for a 30 frame segment of the game
Seaquest. The three screenshots correspond to the frames labeled by A, B, and C respectively.

5.2

Visualizing the Value Function

Figure 3 shows a visualization of the learned value function on the game Seaquest. The figure showsthat the predicted value jumps after an enemy appears on the left of the screen (point A). The agent
then fires a torpedo at the enemy and the predicted value peaks as the torpedo is about to hit theenemy (point B). Finally, the value falls to roughly its original value after the enemy disappears(point C). Figure 3 demonstrates that our method is able to learn how the value function evolves fora reasonably complex sequence of events.
5.3

Main Evaluation

We compare our results with the best performing methods from the RL literature [3, 4]. The method
labeled Sarsa used the Sarsa algorithm to learn linear policies on several different feature sets handengineered for the Atari task and we report the score for the best performing feature set [3]. Contingency used the same basic approach as Sarsa but augmented the feature sets with a learned
representation of the parts of the screen that are under the agent’s control [4]. Note that both of thesemethods incorporate significant prior knowledge about the visual problem by using background subtraction and treating each of the 128 colors as a separate channel. Since many of the Atari games use
one distinct color for each type of object, treating each color as a separate channel can be similar to
producing a separate binary map encoding the presence of each object type. In contrast, our agentsonly receive the raw RGB screenshots as input and must learn to detect objects on their own.
In addition to the learned agents, we also report scores for an expert human game player and a policythat selects actions uniformly at random. The human performance is the median reward achieved
after around two hours of playing each game. Note that our reported human scores are much higher
than the ones in Bellemare et al. [3]. For the learned methods, we follow the evaluation strategy used
in Bellemare et al. [3, 5] and report the average score obtained by running an -greedy policy with
 = 0.05 for a fixed number of steps. The first five rows of table 1 show the per-game average scoreson all games. Our approach (labeled DQN) outperforms the other learning methods by a substantial
margin on all seven games despite incorporating almost no prior knowledge about the inputs.
We also include a comparison to the evolutionary policy search approach from [8] in the last threerows of table 1. We report two sets of results for this method. The HNeat Best score reflects theresults obtained by using a hand-engineered object detector algorithm that outputs the locations and7

RandomSarsa [3]Contingency [4]
DQN
Human
HNeat Best [8]HNeat Pixel [8]DQN Best

B. RiderBreakout

EnduroPong

Q*bertSeaquest

S. Invaders

354
996
1743
4092
7456
3616
1332
5184

1.2
5.2
6
168
31
52
4
225

0
129
159
470
368
106
91
661

−20.4
−19
−17
20
−3
19
−16
21

157
614
960
1952
18900
1800
1325
4500

110
665
723
1705
28010
920
800
1740

179
271
268
581
3690
1720
1145
1075

Table 1: The upper table compares average total reward for various learning methods by runningan -greedy policy with  = 0.05 for a fixed number of steps. The lower table reports results ofthe single best performing episode for HNeat and DQN. HNeat produces deterministic policies thatalways get the same score while DQN used an -greedy policy with  = 0.05.

types of objects on the Atari screen. The HNeat Pixel score is obtained by using the special 8 color
channel representation of the Atari emulator that represents an object label map at each channel.
This method relies heavily on finding a deterministic sequence of states that represents a successful
exploit. It is unlikely that strategies learnt in this way will generalize to random perturbations;
therefore the algorithm was only evaluated on the highest scoring single episode. In contrast, ouralgorithm is evaluated on -greedy control sequences, and must therefore generalize across a wide
variety of possible situations. Nevertheless, we show that on all the games, except Space Invaders,
not only our max evaluation results (row 8), but also our average results (row 4) achieve better
performance.
Finally, we show that our method achieves better performance than an expert human player on
Breakout, Enduro and Pong and it achieves close to human performance on Beam Rider. The games
Q*bert, Seaquest, Space Invaders, on which we are far from human performance, are more challenging because they require the network to find a strategy that extends over long time scales.

6

Conclusion

This paper introduced a new deep learning model for reinforcement learning, and demonstrated its
ability to master difficult control policies for Atari 2600 computer games, using only raw pixels
as input. We also presented a variant of online Q-learning that combines stochastic minibatch updates with experience replay memory to ease the training of deep networks for RL. Our approachgave state-of-the-art results in six of the seven games it was tested on, with no adjustment of thearchitecture or hyperparameters.

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