Principle:Farama Foundation Gymnasium Discrete Action Space

Knowledge Sources	OpenAI Gym Gymnasium Spaces
Domains	Reinforcement_Learning, Space_Definition
Last Updated	2026-02-15 03:00 GMT

Overview

A mathematical representation of a finite set of integers used to define discrete action or observation spaces in reinforcement learning environments.

Description

A Discrete space represents a finite set of consecutive integers $\{a,a+1,\dots ,a+n-1\}$ where n is the number of elements and a is the starting value (default 0). This is the most common action space type for environments with a finite number of distinct actions (e.g., left/right, hit/stand, up/down/left/right).

Key properties:

• n: The number of elements in the space
• start: The smallest element (default 0)
• sample(): Uniform random sampling with optional masking or probability weighting
• contains(): Membership testing

The Discrete space supports action masking (invalid actions set to 0) and probability-weighted sampling for advanced exploration strategies.

Usage

Use this space when the action or observation is one of a finite, enumerable set of choices. This is the standard choice for tabular RL (Q-learning, SARSA), grid-world navigation, and classification-style decisions. For continuous actions, use Box instead.

Theoretical Basis

A discrete space $S=\{a,a+1,\dots ,a+n-1\}$ has uniform sampling probability:

$P(x)=\frac{1}{n},\mathrm{\forall }x\in S$

With an action mask $m\in \{0,1{\}}^n$, sampling is restricted to valid actions:

$P(x|m)=\frac{m_x}{\sum _i{m}_i},\text{if }\sum _i{m}_i>0$

Related Pages

Implemented By

• Implementation:Farama_Foundation_Gymnasium_Discrete_Space