Graph search expands possible states through actions until it finds a goal or exhausts a budget. The representation of state and neighbors determines what solutions can be discovered.

Search Explores Possible States

A heuristic estimates which states seem promising so search spends less effort. It can improve speed but may bias exploration or sacrifice optimality unless its properties are known.

Heuristics Guide Search Without Proving the Answer

MCTS grows a search tree by balancing promising actions with underexplored ones and using simulated outcomes. Its result depends on rollout fidelity, budget, and value estimates.

Monte Carlo Tree Search Allocates Simulation

A planner proposes steps under constraints; an executor validates and performs one step at a time while state may force replanning. A plan is a hypothesis, not authorization.

Plan-and-Execute Separates Deliberation From Action

A reward signal maps outcomes to a value used for learning or selection. If it is only a proxy for the real goal, optimization may exploit the proxy and harm unmeasured outcomes.

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