Signal Processing - November 2017 - 31

danger of suffering from model errors, which
determined. For gradient-based learning,
Searching directly for a
in turn affects the learned policy. Although
this Monte Carlo approximation poses a
policy represented by a
deep neural networks can potentially produce
challenge since gradients cannot pass through
neural network with very
very complex and rich models [14], [55], [75],
these samples of a stochastic function. Theremany parameters can be
sometimes simpler, more data-efficient methfore, we turn to an estimator of the gradient,
difficult and can suffer
ods are preferable [19]. These considerations
known in RL as the REINFORCE rule [97].
from severe local minima. also play a role in actor-critic methods with
Intuitively, gradient ascent using the estimalearned value functions [32], [71].
tor increases the log probability of the sampled action, weighted by the return. More
formally, the REINFORCE rule can be used to compute the graThe rise of DRL
dient of an expectation over a function f of a random variable X
Many of the successes in DRL have been based on scaling
up prior work in RL to high-dimensional problems. This is
with respect to parameters i:
due to the learning of low-dimensional feature representations
d i E X [ f (X; i)] = E X [ f (X; i) d i log p (X)] . (7)
	
and the powerful function approximation properties of neural
networks. By means of representation learning, DRL can deal
efficiently with the curse of dimensionality, unlike tabular and
As this computation relies on the empirical return of a trajectraditional nonparametric methods [7]. For instance, convotory, the resulting gradients possess a high variance. By introduclutional neural networks (CNNs) can be used as components
ing unbiased estimates that are less noisy, it is possible to reduce
of RL agents, allowing them to learn directly from raw, highthe variance. The general methodology for performing this is to
dimensional visual inputs. In general, DRL is based on trainsubtract a baseline, which means weighting updates by an advaning deep neural networks to approximate the optimal policy
tage rather than the pure return. The simplest baseline is the aver*
*
*
*
age return taken over several episodes [97], but there are many
r and/or the optimal value functions V , Q , and A .
more options available [71].

Value functions

Actor-critic methods
It is possible to combine value functions with an explicit representation of the policy, resulting in actor-critic methods,
as shown in Figure 4. The "actor" (policy) learns by using
feedback from the "critic" (value function). In doing so, these
methods tradeoff variance reduction of policy gradients with
bias introduction from value function methods [32], [71].
Actor-critic methods use the value function as a baseline
for policy gradients, such that the only fundamental difference
between actor-critic methods and other baseline methods is
that actor-critic methods utilize a learned value function. For
this reason, we will later discuss actor-critic methods as a subset of policy gradient methods.

The well-known function approximation properties of neural networks led naturally to the use of deep learning to regress functions
for use in RL agents. Indeed, one of the earliest success stories in
RL is TD-Gammon, a neural network that reached expert-level
performance in backgammon in the early 1990s [81]. Using TD
methods, the network took in the state of the board to predict the
probability of black or white winning. Although this simple idea
has been echoed in later work [73], progress in RL research has
favored the explicit use of value functions, which can capture the

Actor
(Policy)

Planning and learning
Given a model of the environment, it is possible to use dynamic programming over all possible actions [Figure 3(a)], sample
trajectories for heuristic search (as was done by AlphaGo
[73]), or even perform an exhaustive search [Figure 3(b)]. Sutton and Barto [78] define planning as any method that utilizes
a model to produce or improve a policy. This includes distribution models, which include T and R, and sample models,
from which only samples of transitions can be drawn.
In RL, we focus on learning without access to the underlying
model of the environment. However, interactions with the environment could be used to learn value functions, policies, and also
a model. Model-free RL methods learn directly from interactions
with the environment, but model-based RL methods can simulate
transitions using the learned model, resulting in increased sample
efficiency. This is particularly important in domains where each
interaction with the environment is expensive. However, learning
a model introduces extra complexities, and there is always the

TD Error
State

Action

Critic
(Value Function)
Reward
Environment

FIGURE 4. The actor-critic setup. The actor (policy) receives a state from
the environment and chooses an action to perform. At the same time, the
critic (value function) receives the state and reward resulting from the
previous interaction. The critic uses the TD error calculated from this information to update itself and the actor. (Figure recreated based on [78].)

IEEE SIGNAL PROCESSING MAGAZINE

|

November 2017

|

31



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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