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The Mountain Red MDP is a deterministic MDP that consists of a car placed stochastically at the bottom of a sinusoidal valley, with the only possible actions being the accelerations that can be applied to the car in either direction. The goal of the MDP is to strategically accelerate the car to reach the goal state on top of the right hill. There are two versions of the mountain car domain in gym: one with discrete actions and one with continuous. This version is the one with discrete actions.

This MDP first appeared in Andrew Moore's PhD Thesis (1990)

@TECHREPORT{Moore90efficientmemory-based,
    author = {Andrew William Moore},
    title = {Efficient Memory-based Learning for Robot Control},
    institution = {University of Cambridge},
    year = {1990}
}

The observation is a ndarray with shape (2,) where the elements correspond to the following:

There are 3 discrete deterministic actions:

Given an action, the mountain car follows the following transition dynamics:

velocity_t+1 = velocity_t + (action - 1) * force - cos(3 * position_t) * gravity

position_t+1 = position_t + velocity_t+1

where force = 0.001 and gravity = 0.0025. The collisions at either end are inelastic with the velocity set to 0 upon collision with the wall. The position is clipped to the range [-1.2, 0.6] and velocity is clipped to the range [-0.07, 0.07].

The goal is to reach the flag placed on top of the right hill as quickly as possible, as such the agent is penalised with a reward of -1 for each timestep.

The position of the car is assigned a uniform random value in [-0.6 , -0.4]. The starting velocity of the car is always assigned to 0.

The episode ends if either of the following happens:

1. Termination: The position of the car is greater than or equal to 0.5 (the goal position on top of the right hill)
2. Truncation: The length of the episode is 200.

gym.make('MountainCar-v0')

• v0: Initial versions release (1.0.0)