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---
name: reward_projection
description: Project late-specified rewards into backward representation coordinates for immediate FB policy adaptation.
---
# Reward Projection
Use this skill after an FB backward embedding has been learned and a reward is specified later. It should not update the reward-free embeddings or run new task-specific RL.
## Inputs
- Backward embeddings `B` indexed by state or goal.
- Reward observations as `{index, reward}` records or a sparse goal index.
## Outputs
- Task vector `z_R` as the weighted sum or average of backward embeddings.
- Provenance describing which reward entries contributed.
## Workflow
1. Validate that all reward indices exist in `B`.
2. Compute `z_R = sum_g B(g) r(g)` for explicit finite rewards.
3. Preserve multi-goal rewards by summing their weighted backward vectors.
4. Return diagnostics and never mutate `F` or `B`.
## Validation
Run `python scripts/project_reward.py --self-test`. The test checks sparse and composite rewards.
## Limitations
For continuous goals this reduced script expects sampled reward observations rather than integrals over an unknown density.
