Signal Processing - November 2017 - 33

TD error based on its own rapidly fluctuating estimates of
the Q-values, the policy network uses the fixed target network. During training, the weights of the target network are
updated to match the policy network after a fixed number of
steps. Both experience replay and target networks have gone
on to be used in subsequent DRL works [19], [44], [50], [93].

Q-function modifications
Considering that one of the key components of the DQN is a
function approximator for the Q-function, it can benefit from
fundamental advances in RL. In [86], van Hasselt showed that
the single estimator used in the Q-learning update rule overestimates the expected return due to the use of the maximum
action value as an approximation of the maximum expected
action value. Double-Q learning provides a better estimate
through the use of a double estimator [86]. While double-Q
learning requires an additional function to be learned, later
work proposed using the already available target network
from the DQN algorithm, resulting in significantly better
results with only a small change in the update step [87].
Yet another way to adjust the DQN architecture is to
decompose the Q-function into meaningful functions, such as
constructing Q r by adding together separate layers that compute the state-value function V r and advantage function A r
[92]. Rather than having to come up with accurate Q-values
for all actions, the duelling DQN [92] benefits from a single
baseline for the state in the form of V r and easier-to-learn
relative values in the form of A r. The combination of the duelling DQN with prioritized experience replay [67] is one of the
state-of-the-art techniques in discrete action settings. Further
insight into the properties of A r by Gu et al. [19] led them to
modify the DQN with a convex advantage layer that extended
the algorithm to work over sets of continuous actions, creating
the normalized advantage function (NAF) algorithm. Benefiting from experience replay, target networks, and advantage
updates, NAF is one of several state-of-the-art techniques in
continuous control problems [19].

Policy search
Policy search methods aim to directly find policies by means
of gradient-free or gradient-based methods. Prior to the current surge of interest in DRL, several successful methods in
DRL eschewed the commonly used backpropagation algorithm in favor of evolutionary algorithms [17], [33], which are
gradient-free policy search algorithms. Evolutionary methods
rely on evaluating the performance of a population of agents.
Hence, they are expensive for large populations or agents with
many parameters. However, as black-box optimization methods, they can be used to optimize arbitrary, nondifferentiable
models and naturally allow for more exploration in the parameter space. In combination with a compressed representation
of neural network weights, evolutionary algorithms can even
be used to train large networks; such a technique resulted in
the first deep neural network to learn an RL task, straight
from high-dimensional visual inputs [33]. Recent work has
reignited interest in evolutionary methods for RL as they can

FIGURE 6. A saliency map of a trained DQN [47] playing Space Invad-

ers [5]. By backpropagating the training signal to the image space, it is
possible to see what a neural-network-based agent is attending to. In
this frame, the most salient points-shown with the red overlay-are the
laser that the agent recently fired and also the enemy that it anticipates
hitting in a few time steps.

potentially be distributed at larger scales than techniques that
rely on gradients [65].

Backpropagation through stochastic functions
The workhorse of DRL, however, remains backpropagation.
The previously discussed REINFORCE rule [97] allows neural
networks to learn stochastic policies in a task-dependent manner, such as deciding where to look in an image to track [69]
or caption [99] objects. In these cases, the stochastic variable
would determine the coordinates of a small crop of the image
and hence reduce the amount of computation needed. This
usage of RL to make discrete, stochastic decisions over inputs
is known in the deep-learning literature as hard attention and is
one of the more compelling uses of basic policysearch methods
in recent years, having many applications outside of traditional
RL domains.

Compounding errors
Searching directly for a policy represented by a neural network
with very many parameters can be difficult and suffer from severe
local minima. One way around this is to use guided policy search
(GPS), which takes a few sequences of actions from another controller (which could be constructed using a separate method, such

IEEE SIGNAL PROCESSING MAGAZINE

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November 2017

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Table of Contents for the Digital Edition of Signal Processing - November 2017

Signal Processing - November 2017 - Cover1
Signal Processing - November 2017 - Cover2
Signal Processing - November 2017 - 1
Signal Processing - November 2017 - 2
Signal Processing - November 2017 - 3
Signal Processing - November 2017 - 4
Signal Processing - November 2017 - 5
Signal Processing - November 2017 - 6
Signal Processing - November 2017 - 7
Signal Processing - November 2017 - 8
Signal Processing - November 2017 - 9
Signal Processing - November 2017 - 10
Signal Processing - November 2017 - 11
Signal Processing - November 2017 - 12
Signal Processing - November 2017 - 13
Signal Processing - November 2017 - 14
Signal Processing - November 2017 - 15
Signal Processing - November 2017 - 16
Signal Processing - November 2017 - 17
Signal Processing - November 2017 - 18
Signal Processing - November 2017 - 19
Signal Processing - November 2017 - 20
Signal Processing - November 2017 - 21
Signal Processing - November 2017 - 22
Signal Processing - November 2017 - 23
Signal Processing - November 2017 - 24
Signal Processing - November 2017 - 25
Signal Processing - November 2017 - 26
Signal Processing - November 2017 - 27
Signal Processing - November 2017 - 28
Signal Processing - November 2017 - 29
Signal Processing - November 2017 - 30
Signal Processing - November 2017 - 31
Signal Processing - November 2017 - 32
Signal Processing - November 2017 - 33
Signal Processing - November 2017 - 34
Signal Processing - November 2017 - 35
Signal Processing - November 2017 - 36
Signal Processing - November 2017 - 37
Signal Processing - November 2017 - 38
Signal Processing - November 2017 - 39
Signal Processing - November 2017 - 40
Signal Processing - November 2017 - 41
Signal Processing - November 2017 - 42
Signal Processing - November 2017 - 43
Signal Processing - November 2017 - 44
Signal Processing - November 2017 - 45
Signal Processing - November 2017 - 46
Signal Processing - November 2017 - 47
Signal Processing - November 2017 - 48
Signal Processing - November 2017 - 49
Signal Processing - November 2017 - 50
Signal Processing - November 2017 - 51
Signal Processing - November 2017 - 52
Signal Processing - November 2017 - 53
Signal Processing - November 2017 - 54
Signal Processing - November 2017 - 55
Signal Processing - November 2017 - 56
Signal Processing - November 2017 - 57
Signal Processing - November 2017 - 58
Signal Processing - November 2017 - 59
Signal Processing - November 2017 - 60
Signal Processing - November 2017 - 61
Signal Processing - November 2017 - 62
Signal Processing - November 2017 - 63
Signal Processing - November 2017 - 64
Signal Processing - November 2017 - 65
Signal Processing - November 2017 - 66
Signal Processing - November 2017 - 67
Signal Processing - November 2017 - 68
Signal Processing - November 2017 - 69
Signal Processing - November 2017 - 70
Signal Processing - November 2017 - 71
Signal Processing - November 2017 - 72
Signal Processing - November 2017 - 73
Signal Processing - November 2017 - 74
Signal Processing - November 2017 - 75
Signal Processing - November 2017 - 76
Signal Processing - November 2017 - 77
Signal Processing - November 2017 - 78
Signal Processing - November 2017 - 79
Signal Processing - November 2017 - 80
Signal Processing - November 2017 - 81
Signal Processing - November 2017 - 82
Signal Processing - November 2017 - 83
Signal Processing - November 2017 - 84
Signal Processing - November 2017 - 85
Signal Processing - November 2017 - 86
Signal Processing - November 2017 - 87
Signal Processing - November 2017 - 88
Signal Processing - November 2017 - 89
Signal Processing - November 2017 - 90
Signal Processing - November 2017 - 91
Signal Processing - November 2017 - 92
Signal Processing - November 2017 - 93
Signal Processing - November 2017 - 94
Signal Processing - November 2017 - 95
Signal Processing - November 2017 - 96
Signal Processing - November 2017 - 97
Signal Processing - November 2017 - 98
Signal Processing - November 2017 - 99
Signal Processing - November 2017 - 100
Signal Processing - November 2017 - 101
Signal Processing - November 2017 - 102
Signal Processing - November 2017 - 103
Signal Processing - November 2017 - 104
Signal Processing - November 2017 - 105
Signal Processing - November 2017 - 106
Signal Processing - November 2017 - 107
Signal Processing - November 2017 - 108
Signal Processing - November 2017 - 109
Signal Processing - November 2017 - 110
Signal Processing - November 2017 - 111
Signal Processing - November 2017 - 112
Signal Processing - November 2017 - 113
Signal Processing - November 2017 - 114
Signal Processing - November 2017 - 115
Signal Processing - November 2017 - 116
Signal Processing - November 2017 - 117
Signal Processing - November 2017 - 118
Signal Processing - November 2017 - 119
Signal Processing - November 2017 - 120
Signal Processing - November 2017 - 121
Signal Processing - November 2017 - 122
Signal Processing - November 2017 - 123
Signal Processing - November 2017 - 124
Signal Processing - November 2017 - 125
Signal Processing - November 2017 - 126
Signal Processing - November 2017 - 127
Signal Processing - November 2017 - 128
Signal Processing - November 2017 - 129
Signal Processing - November 2017 - 130
Signal Processing - November 2017 - 131
Signal Processing - November 2017 - 132
Signal Processing - November 2017 - 133
Signal Processing - November 2017 - 134
Signal Processing - November 2017 - 135
Signal Processing - November 2017 - 136
Signal Processing - November 2017 - 137
Signal Processing - November 2017 - 138
Signal Processing - November 2017 - 139
Signal Processing - November 2017 - 140
Signal Processing - November 2017 - 141
Signal Processing - November 2017 - 142
Signal Processing - November 2017 - 143
Signal Processing - November 2017 - 144
Signal Processing - November 2017 - 145
Signal Processing - November 2017 - 146
Signal Processing - November 2017 - 147
Signal Processing - November 2017 - 148
Signal Processing - November 2017 - 149
Signal Processing - November 2017 - 150
Signal Processing - November 2017 - 151
Signal Processing - November 2017 - 152
Signal Processing - November 2017 - 153
Signal Processing - November 2017 - 154
Signal Processing - November 2017 - 155
Signal Processing - November 2017 - 156
Signal Processing - November 2017 - 157
Signal Processing - November 2017 - 158
Signal Processing - November 2017 - 159
Signal Processing - November 2017 - 160
Signal Processing - November 2017 - 161
Signal Processing - November 2017 - 162
Signal Processing - November 2017 - 163
Signal Processing - November 2017 - 164
Signal Processing - November 2017 - 165
Signal Processing - November 2017 - 166
Signal Processing - November 2017 - 167
Signal Processing - November 2017 - 168
Signal Processing - November 2017 - 169
Signal Processing - November 2017 - 170
Signal Processing - November 2017 - 171
Signal Processing - November 2017 - 172
Signal Processing - November 2017 - 173
Signal Processing - November 2017 - 174
Signal Processing - November 2017 - 175
Signal Processing - November 2017 - 176
Signal Processing - November 2017 - Cover3
Signal Processing - November 2017 - Cover4
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