Frozen Lake¶

Description¶

The game starts with the player at location [0,0] of the frozen lake grid world with the goal located at far extent of the world e.g. [3,3] for the 4x4 environment.

Holes in the ice are distributed in set locations when using a pre-determined map or in random locations when a random map is generated.

The player makes moves until they reach the goal or fall in a hole.

The lake is slippery (unless disabled) so the player may move perpendicular to the intended direction sometimes (see is_slippery).

Randomly generated worlds will always have a path to the goal.

Elf and stool from https://franuka.itch.io/rpg-snow-tileset. All other assets by Mel Tillery http://www.cyaneus.com/.

Action Space¶

The action shape is (1,) in the range {0, 3} indicating which direction to move the player.

• 0: Move left

• 1: Move down

• 2: Move right

• 3: Move up

Observation Space¶

The observation is a value representing the player’s current position as current_row * ncols + current_col (where both the row and col start at 0).

For example, the goal position in the 4x4 map can be calculated as follows: 3 * 4 + 3 = 15. The number of possible observations is dependent on the size of the map.

The observation is returned as an int().

Starting State¶

The episode starts with the player in state [0] (location [0, 0]).

Rewards¶

Reward schedule:

• Reach goal: +1

• Reach hole: 0

• Reach frozen: 0

Episode End¶

The episode ends if the following happens:

• Termination:

  1. The player moves into a hole.

  2. The player reaches the goal at max(nrow) * max(ncol) - 1 (location [max(nrow)-1, max(ncol)-1]).

• Truncation (when using the time_limit wrapper):

  1. The length of the episode is 100 for 4x4 environment, 200 for FrozenLake8x8-v1 environment.

Information¶

step() and reset() return a dict with the following keys:

• p - transition probability for the state.

See is_slippery for transition probability information.

Arguments¶

import gymnasium as gym
gym.make('FrozenLake-v1', desc=None, map_name="4x4", is_slippery=True)

desc=None: Used to specify maps non-preloaded maps.

Specify a custom map.

    desc=["SFFF", "FHFH", "FFFH", "HFFG"].

A random generated map can be specified by calling the function generate_random_map.

from gymnasium.envs.toy_text.frozen_lake import generate_random_map

gym.make('FrozenLake-v1', desc=generate_random_map(size=8))

map_name="4x4": ID to use any of the preloaded maps.

    "4x4":[
        "SFFF",
        "FHFH",
        "FFFH",
        "HFFG"
        ]

    "8x8": [
        "SFFFFFFF",
        "FFFFFFFF",
        "FFFHFFFF",
        "FFFFFHFF",
        "FFFHFFFF",
        "FHHFFFHF",
        "FHFFHFHF",
        "FFFHFFFG",
    ]

If desc=None then map_name will be used. If both desc and map_name are None a random 8x8 map with 80% of locations frozen will be generated.

is_slippery=True: If true the player will move in intended direction with probability of 1/3 else will move in either perpendicular direction with equal probability of 1/3 in both directions.

For example, if action is left and is_slippery is True, then:

• P(move left)=1/3

• P(move up)=1/3

• P(move down)=1/3

Version History¶

• v1: Bug fixes to rewards

• v0: Initial version release