MACHINE LEARNING TECHNIQUES - LASA

More documents

Recommendations

Info

170 7.3 Reinforcement Learning Adapted from [Sutton & Barto, 1998; Kaelbling, Littman & Moore, 1996]. Reinforcement learning is the problem faced by an agent that must learn behavior through trialand-error interactions with a dynamic environment. Reinforcement learning is learning what to do--how to map situations to actions--so as to maximize a numerical reward signal. The learner is not told which actions to take, as in most forms of machine learning, but instead must discover which actions yield the most reward by trying them. In the most interesting and challenging cases, actions may affect not only the immediate reward but also the next situation and, through that, all subsequent rewards. These two characteristics-- trial-and-error search and delayed reward--are the two most important distinguishing features of reinforcement learning. A good way to understand reinforcement learning is to consider some of the examples and possible applications that have guided its development. Consider a master chess player making a move. The choice is informed both by planning-- anticipating possible replies and counter replies--and by immediate, intuitive judgments of the desirability of particular positions and moves. However, a chess player was not born with this knowledge. The player acquired it. A chess player becomes a master only after numerous defeats. It is through these unsuccessful games that the player manages, through a complex process of deduction, to determine which of the numerous steps were misguided and led to the ultimate defeat. Consider a baby managing her first steps. Before walking steadily, the baby is likely to have fallen down numerous times. It is as likely that none of the falls were similar to one another. Thus, a simple associative process would not be sufficient to infer the correct set of actions to undertake in order to achieve a steady walking pattern. In the first example, the reward is a binary value, the success of the game, while in the second; the reward is more continuous (duration of the walk before falling, complete fall versus sitting). A challenge in reinforcement learning is to define the reward. It is clear that the goal of the agent is to maximize the reward. However, how can the agent know when the maximum is reached? Reinforcement learning is different from supervised learning. Supervised learning is learning from examples provided by a knowledgeable external supervisor. This is an important kind of learning, but alone it is not adequate for learning from simply interacting with the world, as in the second example above. In interactive problems it is often impractical to obtain examples of desired behavior that are both correct and representative of all the situations in which the agent has to act. In uncharted territory--where one would expect learning to be most beneficial--an agent must be able to learn from its own experience. One of the challenges that arise in reinforcement learning and not in other kinds of learning is the trade-off between exploration and exploitation. To obtain a lot of reward, a reinforcement learning agent must prefer actions that it has tried in the past and found to be effective in producing reward. But to discover such actions, it has to try actions that it has not selected before. The agent has to exploit what it already knows in order to obtain reward, but it also has to explore in order to make better action selections in the future. The dilemma is that neither exploration nor exploitation can be pursued exclusively without failing at the task. The agent must try a variety of actions and progressively favor those that appear to be best. On a stochastic task, each action must be tried many times to gain a reliable estimate of its expected reward. © A.G.Billard 2004 – Last Update March 2011
171 7.3.1 Principle In reinforcement learning, the purpose or goal of the agent is formalized in terms of a special reward signal passing from the environment to the agent. At each time step, the reward is a r ∈R. Informally, the agent's goal is to maximize the total amount of reward it simple number, t receives. This means maximizing not immediate reward, but cumulative reward in the long run. The reinforcement-learning problem is meant to be a straightforward framing of the problem of learning from interaction to achieve a goal. The learner and decision-maker is called the agent. The thing it interacts with, comprising everything outside the agent, is called the environment. These interact continually, the agent selecting actions and the environment responding to those actions and presenting new situations to the agent. The environment also gives rise to rewards, special numerical values that the agent tries to maximize over time. A complete specification of an environment defines a task, one instance of the reinforcement-learning problem. More specifically, the agent and environment interact at each of a sequence of discrete time . At each time step t , the agent receives some representation of the steps, t = 0,1, 2,3,... environment's state, action, at st ∈ S ∈ A, where ( ) , where S is the set of possible states, and on that basis selects an As is the set of actions available in state s t . One time step later, in t part as a consequence of its action, the agent receives a numerical reward, t itself in a new state s t + . Figure 7-6 diagrams the agent-environment interaction. 1 r ∈R, and finds Figure 7-6: The agent-environment interaction in reinforcement learning. An intuitive way to understand the relation between the agent and its environment is with the following example dialogue. Environment: You are in state 65. You have 4 possible actions. Agent: I'll take action 2. Environment: You received a reinforcement of 7 units. You are now in state 15. You have 2 possible actions. Agent: I'll take action 1. Environment: You received a reinforcement of -4 units. You are now in state 65. You have 4 © A.G.Billard 2004 – Last Update March 2011
Page 1 and 2:
SCHOOL OF ENGINEERING MACHINE LEARN
Page 3 and 4:
3 4. 4 Regression Techniques ......
Page 5 and 6:
5 9.2.2 Probability Distributions,
Page 7 and 8:
7 Journals: • Machine Learning
Page 9 and 10:
9 Performance What would be an opti
Page 11 and 12:
11 1.2.3 Key features for a good le
Page 13 and 14:
13 1.3.2 Crossvalidation To ensure
Page 15 and 16:
15 In particular, we will consider
Page 17 and 18:
17 2.1 Principal Component Analysis
Page 19 and 20:
19 ( ) Xʹ′ = W X − µ (2.6) i
Page 21 and 22:
21 2.1.2.2 Reconstruction error min
Page 23 and 24:
23 PCA is an example of PP approach
Page 25 and 26:
25 Algorithm: If one further assume
Page 27 and 28:
27 The CCA algorithm consists thus
Page 29 and 30:
29 Figure 2-6: Mixture of variables
Page 31 and 32:
31 2.3.2 Why Gaussian variables are
Page 33 and 34:
33 • In our general definition of
Page 35 and 36:
35 2.3.5 ICA Ambiguities We cannot
Page 37 and 38:
37 Denote by g the derivative of th
Page 39 and 40:
39 3 Clustering and Classification
Page 41 and 42:
41 An agglomerative clustering star
Page 43 and 44:
43 3.1.1.1 The CURE Clustering Algo
Page 45 and 46:
45 Disadvantages of hierarchical cl
Page 47 and 48:
47 Cases where K-means might be vie
Page 49 and 50:
49 3.1.4 Clustering with Mixtures o
Page 51 and 52:
51 k ( σ j ) 2 = k ∑ i α = r k
Page 53 and 54:
53 Theα are the so-called mixing c
Page 55 and 56:
55 Figure 3-16: Clustering with 3 G
Page 57 and 58:
57 When the transformation A is lin
Page 59 and 60:
59 C: X → Y ( ) C x K = arg max
Page 61 and 62:
61 Figure 3-18: Linear combination
Page 63 and 64:
63 Figure 3-19: Bayes classificatio
Page 65 and 66:
65 ⎛⎛ min ⎜⎜ w ⎝⎝ N i=
Page 67 and 68:
67 T ( yi − xi w) 2 M ⎛⎛ ⎞
Page 69 and 70:
69 Figure 4-2: Illustration of the
Page 71 and 72:
71 4.4.2 Multi-Gaussian Case It is
Page 73 and 74:
73 5 Kernel Methods These lecture n
Page 75 and 76:
75 The kernel k provides a metric o
Page 77 and 78:
77 M 1 T v = ∑ x ( x ) v M λ i j
Page 79 and 80:
79 1 M The solutions to the dual ei
Page 81 and 82:
81 5.4 Kernel CCA The linear versio
Page 83 and 84:
83 additional ridge parameter induc
Page 85 and 86:
85 Figure 5-3: TOP: Marginal (left)
Page 87 and 88:
87 statistical independence. We def
Page 89 and 90:
89 J j ( µ 1,...., µ K) = ∑∑
Page 91 and 92:
91 A simple pattern recognition alg
Page 93 and 94:
93 ( ) ( , ) f x = sign w x + b (5.
Page 95 and 96:
95 Figure 5-6: A binary classificat
Page 97 and 98:
97 where N is the number of support
Page 99 and 100:
99 5.8 Support Vector Regression In
Page 101 and 102:
101 The optimization problem given
Page 103 and 104:
103 Note that since we never have t
Page 105 and 106:
105 Figure 5-13: Effect of the kern
Page 107 and 108:
107 To better understand the effect
Page 109 and 110:
109 5.9 Gaussian Process Regression
Page 111 and 112:
111 One can then use the above expr
Page 113 and 114:
113 5.9.2 Equivalence of Gaussian P
Page 115 and 116:
115 5.9.3 Curse of dimensionality,
Page 117 and 118:
117 The weight w determines the slo
Page 119 and 120: 119 Figure 5-21: Example of success
Page 121 and 122: 121 • its performance tends to de
Page 123 and 124: 123 neurons. Furthermore, they lear
Page 125 and 126: 125 The sigmoid f x ( x) ( ) = tanh
Page 127 and 128: 127 6.3.2 Information Theory and th
Page 129 and 130: 129 ( R) ⎛⎛det ⎞⎞ I( x, y)
Page 131 and 132: 131 y= ∑ w x ) of Because of the
Page 133 and 134: 133 6.5 Willshaw net David Willshaw
Page 135 and 136: 135 6.6.1 Weights bounds One of the
Page 137 and 138: 137 Figure 6-11: The weight vector
Page 139 and 140: 139 6.6.4 Oja’s one Neuron Model
Page 141 and 142: 141 If y i and y are highly correla
Page 143 and 144: 143 Foldiak’s second model allows
Page 145 and 146: 145 ∂ ∂ J 1 = fy − 1 2 λ 1yf
Page 147 and 148: 147 6.8 The Self-Organizing Map (SO
Page 149 and 150: 149 6. Decrease the size of the nei
Page 151 and 152: 151 the resulting distribution is a
Page 153 and 154: 153 To simplify the description of
Page 155 and 156: 155 C µν −1 where ( ) is the µ
Page 157 and 158: 157 The continuous time Hopfield ne
Page 159 and 160: 159 ∂f If the slope is negative,
Page 161 and 162: 161 7.2 Hidden Markov Models Hidden
Page 163 and 164: 163 Figure 7-2: Schematic illustrat
Page 165 and 166: 165 these two quantities to compute
Page 167 and 168: 167 7.2.4 Decoding an HMM There are
Page 169: 169 7.2.5 Further Readings Rabiner,
Page 173 and 174: 173 general, acting to maximize imm
Page 175 and 176: 175 of reinforcement learning makes
Page 177 and 178: 177 8 Genetic Algorithms We conclud
Page 179 and 180: 179 However, you must define geneti
Page 181 and 182: 181 Often the crossover operator an
Page 183 and 184: 183 ( A λI) x 0 − = (8.5) where
Page 185 and 186: 185 Joint probability: The joint pr
Page 187 and 188: 187 The two most classical distribu
Page 189 and 190: 189 9.2.7 Statistical Independence
Page 191 and 192: 191 1 1 1 1 h x ∫ a b a b 0 a a
Page 193 and 194: 193 9.4 Estimators 9.4.1 Gradient d
Page 195 and 196: 195 9.4.2.1 Maximum Likelihood Mach
Page 197 and 198: 197 10 References • Machine Learn
show all

MACHINE LEARNING TECHNIQUES - LASA

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?