L_p-Adaption

Python implementation of the MATLAB version from:
Asmus, J., Müller, C.L. & Sbalzarini, I.F. L_p-Adaptation: Simultaneous Design Centering and Robustness Estimation of Electronic and Biological Systems. Sci Rep 7, 6660 (2017).

Requirements

The L_p-Adaption needs just a few modules that can be found here in the requirements.txt. You can install them via pip in your selected virtualenv.

pip3 install -r requirements.txt 

Usage of L_p-Adaption

The L_p-Adaption needs an oracle, a pnorm, a feasible starting point, and the parameter options to calculate a design center. The oracle has to be a python function, the starting point a vector with N dimensions, and the parameters are given as a json file for constants and a python file of functions for calculated and recalculated values.

inopts = 'inopts.json'
xstart = [1,1]
LpAdaption(oracle,xstart,inopts)

Executing Examples

When running one of the examples in the 'Lp-Adaption/Examples' folder, make sure that your working directory is the 'Lp-Adaption' directory. Otherwise, referenced files can't be found.

Writing your own L_p-Adaption

It's recommended, to initialize a new class with your oracle as a class function. A template:

import numpy as np
import json
import Vol_lp
import LpBallSampling
import LpAdaption


class LpBallExample():

   def __init__(self, dim: int, pnorm: int, optsFile: str = '../Inputs/example_lpball.json'):
       with open(optsFile) as file:
           self.optsDict = json.load(fp=file)
       self.dim = dim
       self.pn = pnorm

   def lp_adaption(self):
       xstart = [1,-1,1]
       l = LpAdaption.LpAdaption(self.oracle, xstart, inopts=self.optsDict)
       out = l.lpAdaption()

   def oracle(self, x,inopts):
      return sum(x) >= 1

l = LpBallExample(dim=3,pnorm=2)
l.lp_adaption()

Note. that there are some Parameters which are calculated and recalculated through the L_p-Adaption. You can change these parameters in the OptionHandler.py file.

Changeable Parameters

There are two types of parameters one can adapt for the algorithm. First, there are the constant values. They can be given to the algorithm as a dictionary or a .json file respectively. the second type of parameters are the calculated values, which may be used during run time by the algorithm. Therefore, the second type needs a python file with functions for the calculation (OptionHandler.py).

Constant Values

An example for a json file with constant values can be found in the 'Inputs' directory. You can use it directly as a template. The default parameters can be found in options_default.json or DefaultOptions.py. The following Parameters are defined:

• N: Int, Dimension
• maxEval: Int maximum number of function evaluations
• pn: Int, pnorm
• nOut: Int, output dim
• plotting: Bool, plotting on or off
• verboseModulo: log every i-th iteration, MaxEval % verboseModulo == 0
• savingModulo: int, save every i-th iteration, MaxEval % savingModulo ==0
• bSaving: Bool, save data to file
• bSaveCov: Bool, save covariance matrices
• lastSaveAll: save all numLast, r, mu, Q, P_emp
• unfeasibleSave: Bool, save unfeasible points
• averageCovNum: Int, how many of numLast elements are used to get average mu and r
• valP: float, hitting probability
• maxMeanSize: Int, upper bound for interval over which averaging happens
• r: float, starting radius
• initQ, list, starting Q Matrix
• initC: list, starting C Matrix
• maxR: np.inf, maximum radius
• minR: 0, min radius
• maxCond: 2e+20, maximal allowed condition
• N_mu: mean adaptation weight
• N_C: matrix adaptation weight
• hitP_adapt_cond: Bool, if hitting probability is adapted or not
• hitP_adapt:
  • Pvec: list, hitting probability adaption values
  • fixedSchedule: Bool, use fixed schedule for hitting probability adaption
  • maxEvalSchedule: proportion of maxEval for schedule
  • numLastSchedule: over how many samples of each run should be averaged to get radius r and mean mu of found feasible region (if hitP_adapt == 1 and no fixed schedule)
  • testEvery: every i-th iteration it should be tested if step size is in steady state
  • stepSize:
    • deviation: float at which deviation to start step size adaption
  • hitP:
    • deviation: float at which deviation to start hitting probability adaption
  • VolApprox:
    • deviation: float at which deviation to start volume approximation adaption
  • meanOfLast: float, defining how many samples of each run are used for calculating the average if there is no fixed schedule for the changing of the hitting probability (between 0 and 1)
  • deviation_stop: float stop criteria

Calculated Values

List of calculated values with their defaults:

• numLast:

  num_last = max((p['maxEval'] - **1e3 * p['N']), p['maxEval'] * 0.7)

• windowSizeEval:

  windowSizeEval = min(110/p['valP'],p['maxMeanSize'])

• maxR:

  np.inf

• ccov1:

  return 3*0.2/((p['N']+1.3)**2+p['mueff'])

• ccovmu:

  np.seterr(divide='ignore', invalid='ignore')
  return min(1-p['ccov1'], np.divide(3*0.2*np.divide(p['mueff']-2+1,p['mueff']) , ((p['N']+2)**2+p['mueff']*0.2)))

• N_mu:

  return np.exp(1)*p['N']

• Pop_size:

  return max(4 + np.floor(3 * np.log(p['N'])), np.floor(2 /p['valP']))

• beta:

  return 3 * 0.2 / ((p['N'] + 1.3) ** 2 + p['valP'] * p['popSize'])

• ss:

  return 1 + p['beta']*(1-p['valP'])

• sf:

  return 1 - **p['beta']*(p['valP'])

• cp:

  return 1/np.sqrt(p['N'])

• oracle_inopts:

  return []

• stepSize_mean:

  return min(18 / p['valP'], p['maxMeanSize'])

• hitP_mean:

  return min(30 / p['valP'], p['maxMeanSize'])

• hitP_testEvery:

  return min(18 / p['valP'], p['maxMeanSize'])

• volApprox_mean:

  return min(18 / p['valP'], p['maxMeanSize'])

• testStart:

  return max([2*p['hitP_adapt']['stepSize']['meanSize'],
              2*p['hitP_adapt']['hitP']['meanSize'],
              2*p['hitP_adapt']['VolApprox']['meanSize']])