MuZero Latent Model

MuZero extends AlphaZero's tree search to environments with unknown rules by learning dynamics and reward in latent space with three neural functions: ① representation: $s^0_t = h_\theta(s_{t-1}, a_{t-1})$ — compresses (history of) observations into a latent state;② dynamics: $(s^k, r^k) = g_\theta(s^{k-1}, a^k)$ — advances the latent state and predicts reward $p^r$;③ prediction: $(p^k, v^k) = f_\theta(s^k)$ — predicts policy and value $p^v$.

MCTS integration: tree edges are expanded by the networks (not a real environment/rule simulator); during simulation the predicted reward $r^k$ accumulates along paths and the predicted value $v^k$ backs up the return $G$; the root policy comes from a softmax over visit counts. Training regresses the three functions against the MCTS-derived policy target and the real observation's reward/value targets. Key point: reward is predicted in latent space by $g_\theta$ — there is no explicit model of the real environment's reward — so planning works without a known reward function.

board games (chess/shogi/Go at superhuman level), Atari pixel inputs, tasks with unknown rules or rewards; classic interview question: 'how does MuZero remove the explicit rules after AlphaZero?'

AlphaZero relies on a known environment (rules + simulator) for tree search; MuZero replaces the simulator with a latent model, bringing MCTS to real-world tasks with unknown rules and rewards while retaining superhuman play — trading model bias for generality.

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