{"id":"search-value-policy-boundary","name":"Search, value estimates and selected actions","shortName":"Search and value","role":"Explains how a system can spend additional computation selecting an action after receiving an observation.","description":"A policy selects an action. Search evaluates possible continuations before that selection, using a transition model and a value estimate at the explored boundary. In this rule-defined tic-tac-toe specimen, legal moves change a nine-cell board, players alternate, X maximizes and O minimizes a score. Terminal wins receive exact ±100 and draws receive zero. At a truncated leaf, an explicitly authored open-line heuristic supplies a provisional value. Deeper search may replace that guess with a different consequence, at a cost in visited nodes. The heuristic is not learned. Research systems such as AlphaZero combine learned value/policy functions with search; their training and search results are not reproduced by this small example.","mechanism":["Read the board, infer the next player from legal move counts and enumerate legal actions.","Apply each action to a separate board and alternate the maximizing/minimizing player.","Use exact terminal outcomes when available; at the selected depth, use the declared heuristic instead.","Choose the action under the resulting values and count the visited states. Preserve the original board for comparison."],"learningObjective":"Trace legal game actions through a bounded alternating-player search and distinguish terminal evidence from a truncated heuristic.","engineeringExample":"The displayed position has X at opposite corners and O in the center, so O moves next. Compare lookahead depths 1 through 5 and inspect each legal action’s value and visited-node count. A separate exact test uses an immediate X winning row and verifies that the winning move has value +100 regardless of the nonterminal heuristic.","evidenceNotes":"The workbench executes the declared small mechanism. Numeric examples are authored and independently checked, not measurements from the cited research. Finite deterministic perfect-information game, alternating players and a declared fixed heuristic. This is minimax teaching search, not AlphaZero or a learned planning system.","specs":[{"label":"Teaching specimen","value":"Search and value","context":"The displayed position has X at opposite corners and O in the center, so O moves next. Compare lookahead depths 1 through 5 and inspect each legal action’s value and visited-node count. A separate exact test uses an immediate X winning row and verifies that the winning move has value +100 regardless of the nonterminal heuristic."},{"label":"Evidence boundary","value":"Explicit computed example","context":"Finite deterministic perfect-information game, alternating players and a declared fixed heuristic. This is minimax teaching search, not AlphaZero or a learned planning system."}],"interfaces":[{"name":"Inputs and convention","direction":"in","signal":"Read the board, infer the next player from legal move counts and enumerate legal actions."},{"name":"Computed result and scope","direction":"out","signal":"Trace legal game actions through a bounded alternating-player search and distinguish terminal evidence from a truncated heuristic."}],"tradeoff":"More search can improve a decision when the transition/value assumptions are useful, but consumes time and can amplify a wrong model. More visited nodes are not evidence of better real-world reasoning.","whyAI":"Inference-time selection, planning and tool policies can involve additional computation beyond one forward pass. Their benefits require task-specific verification and explicit environmental semantics.","misconception":"Searching at inference time is not the same operation as updating learned parameters. An authored heuristic must not be presented as a trained value function.","check":{"question":"What changes when lookahead depth increases in this specimen?","options":["The evaluated continuation tree and computation spent selecting an action","The fixed heuristic is automatically trained","The rules of the environment change"],"answer":0,"explanation":"The evaluated continuation tree and computation spent selecting an action. Finite deterministic perfect-information game, alternating players and a declared fixed heuristic. This is minimax teaching search, not AlphaZero or a learned planning system."},"prerequisites":[],"related":["evaluation","tool-loop","loss-optimizer"],"sources":[{"title":"Silver et al. · AlphaZero","url":"https://arxiv.org/abs/1712.01815"}],"level":"model","scale":"Mathematical and data space; dimensions are not physical distance","kind":"model","branch":"contrasting-ai-methods","subbranch":"Search and value","workstream":"W11","visualFamily":"mathematical","labId":"library","labScope":"Open Mathematical foundations for the bounded executable mechanism and its record. General numerical labs are an additional reference library.","science":[{"title":"Search, value estimates and selected actions","equation":"Use terminal utility, or a boundary heuristic when depth is zero, otherwise alternate maximizing and minimizing over legal transitions.","explanation":"The displayed position has X at opposite corners and O in the center, so O moves next. Compare lookahead depths 1 through 5 and inspect each legal action’s value and visited-node count. A separate exact test uses an immediate X winning row and verifies that the winning move has value +100 regardless of the nonterminal heuristic.","assumptions":"Finite deterministic perfect-information game, alternating players and a declared fixed heuristic. This is minimax teaching search, not AlphaZero or a learned planning system."}]}