Rescorlar-wagner模型

Rescor

1. 动物中的强化学习

动物心理学家发现，当多个刺激同时出现时，强化学习中存在三种不同的效应：遮蔽效应（Overshadowing）、阻断效应（Blocking）和抑制效应（Inhibition）。

遮蔽效应是指当在训练阶段两个刺激（A和B）同时出现并与一个结果相关联时，相对于单独对A或B进行条件反射的情况，对A或B的学习效果会因为与另一个刺激的复合条件反射而减弱。例如，如果光（A）和声音（B）同时作为条件刺激（CS）与食物（无条件刺激，UCS）配对，动物对声音（B）的条件反应（CR）会比单独呈现声音时弱。

阻断效应是指当一个条件刺激（CS1）已经与无条件刺激（UCS）建立了强烈的关联后，再引入一个新的条件刺激（CS2）时，CS2很难再与UCS建立关联。也就是说，CS1“阻断”了CS2的学习。例如，如果声音（CS1）已经与食物（UCS）配对并引发了唾液分泌（CR），然后再引入光（CS2）与声音一起出现并继续与食物配对，动物只会对声音反应而不会对光产生条件反应。

抑制效应是指一个刺激通过与另一个刺激的关联，抑制了对某个结果的预期。例如，如果光（CS1）与食物（UCS）配对引发唾液分泌（CR），然后再引入声音（CS2）与光一起出现，但这次没有食物出现，动物在测试阶段只会对CS1产生条件反应，而对CS2无反应，甚至会产生相反的条件反应（见表1）。

效应

阶段 1

阶段 2

学习测试

遮蔽效应

[A + B] →食物(UCS)

[A]中等; [B]中等

阻断效应

[A] → UCS

[A + B] → UCS

[A]强; [B]无

抑制效应

[A] → UCS

[A + B] → 0

[A]强[B]无/ [A]强[B]负

A:光； B: 声音； UCS: 无条件刺激; [A] 或者 [B] 代表光或者声音单独出现；[A + B]代表光和声音一起出现。

2. Rescorlar-wagner模型

由之前的章节得到心理学中强化学习的最简递推公式： $V_t=V_{t-1}+a*(r_t - V_{t-1})$ ，被称为简单强化学习模型（navie reinforcement learning model）。但是简单的强化学习（PEi = ri − ；i = Vi -1+ ）无法解释以上三种条件反射现象。

以下通过Python代码模拟基于简单强化学习模型的遮蔽效应的形成过程。

# Naïve model

from scipy.stats import bernoulli
import numpy as np
import matplotlib.pyplot as plt

def overshadow(T):
       '''
       T: number of trials
       '''
      r = np.ones(T) # (T,)维全是1的数组
      A = np.ones(T) # (T,)维全是1的数组
      B = np.ones(T) # (T,)维全是1的数组
      return r, A, B

a = 0.05 # learning rate
T = 100 # number of trials

r, A, B = overshadow(T)

Va = np.empty(T)
Vb = np.empty(T)

for i in range(T): # loop trials
    if i == 0:
        Va[0] = 0 + a*(r[0]-0)
        Vb[0] = 0 + a*(r[0]-0)
    else:
        Va[i] = Va[i-1] + a*(r[i]-Va[i-1])
        Vb[i] = Vb[i-1] + a*(r[i]-Vb[i-1])

plt.plot(r, '-k', label='reward')
plt.plot(Va, linewidth=10, label='Va')
plt.plot(Vb, linewidth=2, label='Vb')
plt.xlabel('Trials')
plt.ylabel('Value')
plt.legend()
```

PE[i] = r[i]-(Va[i-1]A[i]+Vb[i-1]B[i])

Va[i] = Va[i-1] + aPE[i] * A[i]

Vb[i] = Vb[i-1] + aPE[i] * B[i]

RW模型能成功解释上述三种现象。以下通过Python代码模拟基于RW模型的遮蔽效应，阻断效应和抑制效应的形成过程。

# RW model-Overshadowing

a = 0.05 # learning rate
T = 100 # how many trials

r, A, B = overshadow(T)

Va = np.empty(T)
Vb = np.empty(T)

for i in range(T): # loop trials
    if i == 0:
        Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
        Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
    else:
        PE = r[i]-(Va[i-1]*A[i]+Vb[i-1]*B[i])
        Va[i] = Va[i-1] + a*PE * A[i]
        Vb[i] = Vb[i-1] + a*PE * B[i]
        
plt.plot(r, '-k', label='reward')
plt.plot(Va, linewidth=10, label='Va')
plt.plot(Vb, linewidth=2, label='Vb')
plt.xlabel('Trials')
plt.ylabel('Value')
plt.legend()

def block(T):
    T1 = round(T/2) # round是取整数的意思
    # phase 1: A -> R
    r1 = np.ones(T1)
    A1 = np.ones(T1)
    B1 = np.zeros(T1)
    # phase 2: A, B -> R
    r2 = np.ones(T-T1)
    A2 = np.ones(T-T1)
    B2 = np.ones(T-T1)
    # combine two phases
    r = np.hstack((r1, r2))
    A = np.hstack((A1, A2))
    B = np.hstack((B1, B2))
    return r, A, B
    
a = 0.05 # learning rate
T = 1000 # how many trials

r, A, B = block(T)

Va = np.empty(T)
Vb = np.empty(T)

for i in range(T): # loop trials
    if i == 0:
        Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
        Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
    else:
        PE = r[i]-Va[i-1]*A[i]-Vb[i-1]*B[i]
        Va[i] = Va[i-1] + a*PE * A[i]
        Vb[i] = Vb[i-1] + a*PE * B[i]

plt.plot(r, '-k', label='reward')
plt.plot(Va, linewidth=10, label='Va')
plt.plot(Vb, linewidth=2, label='Vb')
plt.xlabel('Trials')
plt.ylabel('Value')
plt.legend()

def inhibition(T):
    r = np.empty(T)
    A = np.empty(T)
    B = np.empty(T)
    for i in range(T):
        if bernoulli.rvs(0.5, 1)==1:
            # A -> R trial
            r[i] = 1
            A[i] = 1
            B[i] = 0
        else:
            # A,B -> 0 trial
            r[i] = 0
            A[i] = 1
            B[i] = 1
    return r, A, B
    
a = 0.05 # learning rate
T = 1000 # how many trials

r, A, B = inhibition(T)

Va = np.empty(T)
Vb = np.empty(T)

for i in range(T): # loop trials
    if i == 0:
        Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
        Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i])
    else:
        PE = r[i]-Va[i-1]*A[i]-Vb[i-1]*B[i]
        Va[i] = Va[i-1] + a*PE * A[i]
        Vb[i] = Vb[i-1] + a*PE * B[i]

#plt.plot(r, '-k', label='reward')
plt.plot(Va, linewidth=10, label='Va')
plt.plot(Vb, linewidth=2, label='Vb')
plt.xlabel('Trials')
plt.ylabel('Value')
plt.legend()

最后更新于4个月前

# Naïve model from scipy.stats import bernoulli import numpy as np import matplotlib.pyplot as plt def overshadow(T): ''' T: number of trials ''' r = np.ones(T) # (T,)维全是1的数组 A = np.ones(T) # (T,)维全是1的数组 B = np.ones(T) # (T,)维全是1的数组 return r, A, B a = 0.05 # learning rate T = 100 # number of trials r, A, B = overshadow(T) Va = np.empty(T) Vb = np.empty(T) for i in range(T): # loop trials if i == 0: Va[0] = 0 + a*(r[0]-0) Vb[0] = 0 + a*(r[0]-0) else: Va[i] = Va[i-1] + a*(r[i]-Va[i-1]) Vb[i] = Vb[i-1] + a*(r[i]-Vb[i-1]) plt.plot(r, '-k', label='reward') plt.plot(Va, linewidth=10, label='Va') plt.plot(Vb, linewidth=2, label='Vb') plt.xlabel('Trials') plt.ylabel('Value') plt.legend() ```

# RW model-Overshadowing a = 0.05 # learning rate T = 100 # how many trials r, A, B = overshadow(T) Va = np.empty(T) Vb = np.empty(T) for i in range(T): # loop trials if i == 0: Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) else: PE = r[i]-(Va[i-1]*A[i]+Vb[i-1]*B[i]) Va[i] = Va[i-1] + a*PE * A[i] Vb[i] = Vb[i-1] + a*PE * B[i] plt.plot(r, '-k', label='reward') plt.plot(Va, linewidth=10, label='Va') plt.plot(Vb, linewidth=2, label='Vb') plt.xlabel('Trials') plt.ylabel('Value') plt.legend()

def block(T): T1 = round(T/2) # round是取整数的意思 # phase 1: A -> R r1 = np.ones(T1) A1 = np.ones(T1) B1 = np.zeros(T1) # phase 2: A, B -> R r2 = np.ones(T-T1) A2 = np.ones(T-T1) B2 = np.ones(T-T1) # combine two phases r = np.hstack((r1, r2)) A = np.hstack((A1, A2)) B = np.hstack((B1, B2)) return r, A, B a = 0.05 # learning rate T = 1000 # how many trials r, A, B = block(T) Va = np.empty(T) Vb = np.empty(T) for i in range(T): # loop trials if i == 0: Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) else: PE = r[i]-Va[i-1]*A[i]-Vb[i-1]*B[i] Va[i] = Va[i-1] + a*PE * A[i] Vb[i] = Vb[i-1] + a*PE * B[i] plt.plot(r, '-k', label='reward') plt.plot(Va, linewidth=10, label='Va') plt.plot(Vb, linewidth=2, label='Vb') plt.xlabel('Trials') plt.ylabel('Value') plt.legend()

def inhibition(T): r = np.empty(T) A = np.empty(T) B = np.empty(T) for i in range(T): if bernoulli.rvs(0.5, 1)==1: # A -> R trial r[i] = 1 A[i] = 1 B[i] = 0 else: # A,B -> 0 trial r[i] = 0 A[i] = 1 B[i] = 1 return r, A, B a = 0.05 # learning rate T = 1000 # how many trials r, A, B = inhibition(T) Va = np.empty(T) Vb = np.empty(T) for i in range(T): # loop trials if i == 0: Va[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) Vb[0] = 0 + a*(r[0] - 0 * A[i] - 0 * B[i]) else: PE = r[i]-Va[i-1]*A[i]-Vb[i-1]*B[i] Va[i] = Va[i-1] + a*PE * A[i] Vb[i] = Vb[i-1] + a*PE * B[i] #plt.plot(r, '-k', label='reward') plt.plot(Va, linewidth=10, label='Va') plt.plot(Vb, linewidth=2, label='Vb') plt.xlabel('Trials') plt.ylabel('Value') plt.legend()