Notation and conventions

OGym calls the agent-visible observation a state in its Rust API. This documentation writes it as \(s_t\), while \(x_t\) denotes a backend’s latent state when the distinction matters. An interaction is

\[ (s_{t+1}, r_t, d_t, i_t) = \operatorname{step}(s_t, a_t), \]

where \(a_t\) is the action, \(r_t\) the reward, \(d_t\) the Terminal status, and \(i_t\) the environment-specific information value.

• Terminate means an environment-defined terminal event occurred.
• Truncate means an external horizon was reached.
• Both records both events on the same transition.
• Ongoing records neither event.

Intervals use \([l,h]\) for inclusive space bounds and \((l,h)\) when the health test uses strict inequalities. clip(x,l,h) limits a scalar to that interval. \(\lVert x\rVert_2\) is the Euclidean norm and \(\lVert x\rVert_2^2=\sum_i x_i^2\).

For MuJoCo, \(q\), \(\dot q\), and \(u\) denote generalized positions, velocities, and actuator controls. A default-model dimension is not a promise for custom XML: the action length is always nu, and observation length is assembled from the loaded model.