OpenAI Gym: Pendulum-v0

This notebook demonstrates how grammar-guided genetic programming (G3P) can be used to solve the Pendulum-v0 problem from OpenAI Gym. This is achieved by searching for a small program that defines an agent, who uses an algebraic expression of the observed variables to decide which action to take in each moment.

Caution: This notebook was run with gym v0.20.0 (pip install gym==0.20.0) and pyglet v1.5.27 (pip install pyglet==1.5.27). Gym deprecated “Pendulum-v0” from v0.20.0 to v.0.21.0. Gym changed its API from v0.25.2 to v0.26.0. Pyglet changed its API from 1.5.27 to 2.0.0.

References

• OpenAI Gym website

  • Classic problems from control theory: an overview of environments

  • Pendulum-v0: the environment solved here

• GitHub

  • Pendulum-v1: details on the next version of the environment solved here

  • Leaderboard: community wiki to track user-provided solutions

  • Example solution: a fixed policy written by Zhiqing Xiao

import time
import warnings

import alogos as al
import gym
import numpy as np
import unified_map as um

warnings.filterwarnings('ignore')

Preparation

1) Environment

Pendulum-v0: The aim is to swing up a frictionless pendulum and keep it standing upright there, starting from random position and velocity. The agent observes the current position and velocity of the pendulum. It can act by applying limited torque to the joint (continuous value between -2 to +2)

env = gym.make('Pendulum-v0')

2) Functions to run single or multiple simulations

It allows an agent to act in an environment and collect rewards until the environment signals it is done.

def simulate_single_run(env, agent, render=False):
    observation = env.reset()
    episode_reward = 0.0
    while True:
        action = agent.decide(observation)
        observation, reward, done, info = env.step(action)
        episode_reward += reward
        if render:
            time.sleep(0.03)
            env.render()
        if done:
            break
    env.close()
    return episode_reward

def simulate_multiple_runs(env, agent, n):
    total_reward = sum(simulate_single_run(env, agent) for _ in range(n))
    mean_reward = total_reward / n
    return mean_reward

Example solutions

num_sim = 500

1) By Zhiqing Xiao

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        flip = (y < 0.)
        if flip:
            y *= -1. # now y >= 0
            angle_velocity *= -1.
        angle = np.arcsin(y)
        if x < 0.:
            angle = np.pi - angle
        if (angle < -0.3 * angle_velocity) or \
                (angle > 0.03 * (angle_velocity - 2.5) ** 2. + 1. and \
                angle < 0.15 * (angle_velocity + 3.) ** 2. + 2.):
            force = 2.
        else:
            force = -2.
        if flip:
            force *= -1.
        action = np.array([force,])
        return action

agent = Agent()
simulate_multiple_runs(env, agent, num_sim)

-146.6261378431444

2) By previous runs of evolutionary optimization

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = (6.46/((4.45**(5.67/8.42))/((((y-y)*1.50)-(((x/x)/x)*angle_velocity))-((5.40*x)*y))))
        action = [min(max(output, -2.0), 2.0)]
        return action

agent = Agent()
simulate_multiple_runs(env, agent, num_sim)

-185.80858672911128

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = ((x/(((2.29-4.83)+y)/(angle_velocity+(8.50*(9.86/0.28)))))*(y+angle_velocity))
        action = [min(max(output, -2.0), 2.0)]
        return action

agent = Agent()
simulate_multiple_runs(env, agent, num_sim)

-216.15272672117865

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = (((((7.05/(x+(6.66/1.04)))-angle_velocity)-((y+y)+x))*3.04)/x)
        action = [min(max(output, -2.0), 2.0)]
        return action

agent = Agent()
simulate_multiple_runs(env, agent, num_sim)

-264.6755941288853

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = ((((2.05*x)-x)*((x-6.40)-(angle_velocity/y)))/y)
        action = [min(max(output, -2.0), 2.0)]
        return action

agent = Agent()
simulate_multiple_runs(env, agent, num_sim)

-322.65006620221567

Definition of search space and goal

1) Grammar

This grammar defines the search space: a Python program that creates an Agent who uses an algebraic expression of the observed variables to decide how to act in each situation.

ebnf_text = """
program = L0 NL L1 NL L2 NL L3 NL L4 NL L5

L0 = "class Agent:"
L1 = "    def decide(self, observation):"
L2 = "        x, y, angle_velocity = observation"
L3 = "        output = " EXPR
L4 = "        action = [min(max(output, -2.0), 2.0)]"
L5 = "        return action"

NL = "\n"

EXPR = VAR | CONST | "(" EXPR OP EXPR ")"
VAR = "x" | "y" | "angle_velocity"
CONST = DIGIT "." DIGIT DIGIT
OP = "+" | "-" | "*" | "/" | "**"
DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
"""

grammar = al.Grammar(ebnf_text=ebnf_text)

2) Objective function

The objective function gets a candidate solution (=a string of the grammar’s language) and returns a fitness value for it. This is done by 1) executing the string as a Python program, so that it creates an agent object, and then 2) using the agent in multiple simulations to see how good it can handle different situations: the higher the total reward, the better is the candidate.

def string_to_agent(string):
    local_vars = dict()
    exec(string, None, local_vars)
    Agent = local_vars['Agent']
    return Agent()


def objective_function(string):
    agent = string_to_agent(string)
    avg_reward = simulate_multiple_runs(env, agent, 15)
    return avg_reward

Generation of a random solution

Check if grammar and objective function work as intended.

random_string = grammar.generate_string()
print(random_string)

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = ((angle_velocity/y)**angle_velocity)
        action = [min(max(output, -2.0), 2.0)]
        return action

objective_function(random_string)

nan

Search for an optimal solution

Evolutionary optimization with random variation and non-random selection is used to find increasingly better candidate solutions.

1) Parameterization

ea = al.EvolutionaryAlgorithm(
    grammar, objective_function, 'max',
    max_or_min_fitness=-180, population_size=50, offspring_size=50,
    evaluator=um.univariate.parallel.futures, verbose=True)

2) Run

best_ind = ea.run()

Progress         Generations      Evaluations      Runtime (sec)    Best fitness
..... .....      10               369              25.2             -1186.9689994988496
..... .....      20               540              33.5             -727.2836108335539
..... .....      30               836              47.9             -378.6647331268654
..... .....      40               1193             67.7             -286.09358866928585
..... .....      50               1465             81.4             -240.8040736173183
..... .....      60               1780             97.0             -239.95336646733077
..... ..

Finished         67               1990             111.1            -173.8957367860315

3) Result

string = best_ind.phenotype
print(string)

class Agent:
    def decide(self, observation):
        x, y, angle_velocity = observation
        output = (((y*((angle_velocity*8.64)-5.86))-y)-(angle_velocity/(0.05*x)))
        action = [min(max(output, -2.0), 2.0)]
        return action

agent = string_to_agent(string)
simulate_multiple_runs(env, agent, 100)

-232.48567351045173

simulate_single_run(env, agent, render=True)

-375.62393381779486