Equation 9 · Part 3 · From Scripted Bots to Autonomous Agents: A History of AI Agent Architecture

Symbol a_t

Q(s_t,a_t) \leftarrow Q(s_t,a_t) + \alpha\Big[r_{t+1} + \gamma \max_{a} Q(s_{t+1},a) - Q(s_t,a_t)\Big].

a_t

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$a_t$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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$a_t$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol a_tArticle meaning

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…each discrete time step, with the agent’s goal defined as maximizing cumulative reward rather than satisfying a hand-specified goal predicate [ 3 ] . The canonical learning rule for estimating the value of taking action $a_t$ in state $s_t$ , temporal-difference Q-learning, updates an estimate toward a bootstrapped target rather than waiting for a final outcome: $Q(s_t,a_t) \leftarrow Q(s_t,a_t) + \alpha\Big[r_{t+1} + \gamma \max_{a} Q(s_{t+1},a) - Q(s_t,a_t)\Big]$ . That equation is the real content of the RL-era architecture, not decoration: the agent’s decision rule is now a function fit…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[3] Reinforcement Learning: An Introduction, Second Edition ↗

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