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Published equation contexts

at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at)a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t)

Why this formula appears here

An agent trajectory can be represented as at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at)a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t). where the model policy chooses an action, environment E executes it against state sts_t , and the result becomes the next observation. This closes a feedback loop absent from one-shot completion.

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o≤to_{\le t}

Symbol o_ ≤ t

o_ ≤ t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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hth_t

Symbol h_t

hth_t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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Published contexts (1)

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at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at),a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t),

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

An agent trajectory can be represented as at∼πθ(a∣o≤t,ht,g),ot+1=E(st,at)a_t\sim\pi_\theta(a\mid o_{\le t},h_t,g), \qquad o_{t+1}=E(s_t,a_t). where the model policy chooses an action, environment E executes it against state sts_t , and the result becomes the next observation. This closes a feedback loop absent from one-shot completion.

Meanings in this article

  • sts_t: the environment e executes it against state.
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