Gradient-based Planning for World Models at Longer Horizons
- Source
- bair.berkeley.edu
- Date

Context
A model that predicts future events still needs a planner to choose actions. GRASP tackles this by revising proposed intermediate states and actions together, allowing work on different times in a plan to run in parallel. The Berkeley AI Research explanation describes why this can help when a goal requires a long sequence of moves.
The difficulty is that optimization can exploit errors in a learned simulator. GRASP limits a sensitive feedback path through the simulated state, introduces random changes to explore alternatives, and periodically refines complete simulated trajectories. In the reported Push-T task, it achieved higher success rates than the compared planners at horizons of 50 to 80 steps, while remaining far from solving every attempt.
- Long-horizon planning through a world model suffers exploding/vanishing gradients because the Jacobian with respect to early actions is a product of per-step Jacobians whose conditioning scales exponentially with the planning horizon.
- GRASP's key trick is stopping gradients into the state input of the world model, trusting only action gradients, because states sit on a low-dimensional manifold with adversarial-example-like brittleness in directions orthogonal to it, which the action space doesn't share.
- Because the naive stop-gradient objective has a trivial minimum (stay put, then jump to the goal on the last step), GRASP adds a dense per-timestep goal term to every predicted state, balanced against the stop-gradient dynamics loss.
- On the Push-T at horizon 80, GRASP hit a 10.4% success rate in a median 58.9s, versus CEM's 2.8%/132.2s and LatCo's 0.0%; at horizon 40, GRASP matched CEM's roughly 60% success rate in about a quarter of the time (8.5s vs 35.3s).
- GRASP periodically breaks from its fast lifted-state optimization to run a short refinement phase using the true serial rollout gradient, to keep the lifted trajectory in dynamics actually reachable by a real rollout.
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