旋转优化器的域？

Question

我很难弄清楚如何在参数优化方法上设置界限(min/max)。旋转是优化算法：https://www.youtube.com/watch?v=2uQ2BSzDvXs。如何确保p(参数)保持在某个域中？下面是我在Python中的Twiddle实现：

def twiddle(objFunction, args, init=0.5, tolerance=0.00001, domain=(0,float("inf"))):
  """Optimize a single parameter given an objective function.

  This is a local hill-climbing algorithm. Here is a simple description of it:
  https://www.youtube.com/watch?v=2uQ2BSzDvXs

  @param args       (tuple)   Arguments necessary for the objective function.

  @param tolerance  (float)   Number used to determine when optimization has
                              converged to a sufficiently good score.

  @param objFunction(function)Objective Function used to quantify how good a
                              particular parameter choice is.

  @param init       (float)   Initial value of the parameter.

  @param domain     (tuple)   Domain of parameter values, as (min, max).

  @return (dict) Contains:
        "parameter" (float)   Threshold that returns the largest score from the
                              Objective function.

        "score"     (float)   The score from the objective function given the
                              threshold.
  """
  pastCalls = {}
  x = init
  delta = 0.1
  bestScore = objFunction(x, args)

  pastCalls[x] = bestScore

  while delta > tolerance: #and x >= domain[0]+tolerance and x <= domain[1]-tolerance:
    x += delta

    if x not in pastCalls:
      score = objFunction(x, args)
      pastCalls[x] = score

    score = pastCalls[x]

    if score > bestScore:
      bestScore = score
      delta *= 2

    else:
      x -= 2*delta

      if x not in pastCalls:
        score = objFunction(x, args)
        pastCalls[x] = score

      score = pastCalls[x]

      if score > bestScore:
        bestScore = score
        delta *= 2
      else:
        x += delta
        delta *= 0.5

    print "Parameter:", x
    print "Best score:", bestScore
    print "delta:", delta
    print

  return {"parameter": x,
          "score": bestScore}

例如，我想以objFunction的形式运行正弦函数，但是域设置为0，2*pi。

Answer 1

明白了!与@AlexMartelli的评论类似，该算法需要防止每次递增/递减到x时超出界限。为了保持爬山算法的核心功能，必须将步长delta调整为当前位置与外部边界之间距离的一半。这样，算法仍然倾向于沿边界方向移动，如果最大值在边界处，则可以到达，必要时还可以从边界移回。代码如下：

def twiddle(objFunction, args, init=0.5, tolerance=0.00001, domain=(float("-inf"), float("inf"))):
  """Optimize a single parameter given an objective function.

  This is a local hill-climbing algorithm. Here is a simple description of it:
  https://www.youtube.com/watch?v=2uQ2BSzDvXs

  @param args       (tuple)   Arguments necessary for the objective function.

  @param tolerance  (float)   Number used to determine when optimization has
                              converged to a sufficiently good score.

  @param objFunction(function)Objective Function used to quantify how good a
                              particular parameter choice is.

  @param init       (float)   Initial value of the parameter.

  @param domain     (tuple)   Domain of parameter values, as (min, max).

  @return (dict) Contains:
        "parameter" (float)   Threshold that returns the largest score from the
                              Objective function.

        "score"     (float)   The score from the objective function given the
                              threshold.
  """
  pastCalls = {}
  x = init
  delta = 0.1
  bestScore = objFunction(x, args)

  pastCalls[x] = bestScore

  while delta > tolerance:

    # Keep x within bounds
    if x+delta > domain[1]:
      delta = abs(domain[1] - x) / 2
    x += delta

    if x not in pastCalls:
      score = objFunction(x, args)
      pastCalls[x] = score

    score = pastCalls[x]

    if score > bestScore:
      bestScore = score
      delta *= 2

    else:
      # Keep x within bounds
      if x-delta < domain[0]:
        delta = abs(domain[0] - x) / 2
      x -= 2*delta

      if x not in pastCalls:
        score = objFunction(x, args)
        pastCalls[x] = score

      score = pastCalls[x]

      if score > bestScore:
        bestScore = score
        delta *= 2
      else:
        x += delta
        delta *= 0.5

    print "Parameter:", x
    print "Best score:", bestScore
    print "Step size:", delta
    print

  return {"parameter": x,
          "score": bestScore}