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name: linear_reward_successor_features description: Compute linear multitask rewards, successor-feature values, and vector Bellman targets for USFA-style reinforcement-learning tasks.

Linear Reward Successor Features

Use this skill when a recovery or implementation needs the Universal Successor Features contract r_w = phi^T w and Q = psi^T w. Do not use it to choose candidate GPI policies; that belongs to the GPI action-selection skill.

Inputs

• phi: transition feature vector.
• w: task reward-weight vector.
• psi: successor-feature vector for (state, action, z).
• next_psi: bootstrap successor-feature vector, or zeros for terminal transitions.
• gamma: discount factor.

Outputs

• Scalar linear reward.
• Scalar Q value.
• Vector Bellman target.
• Vector TD error.

Workflow

1. Validate equal vector dimensions.
2. Compute reward = dot(phi, w).
3. Compute q_value = dot(psi, w).
4. Compute target = phi + gamma * next_psi unless terminal.
5. Compute td_error = target - psi.

Validation

Run:

python tests/test_successor_features.py

Limitations

This skill assumes observable transition features and linear rewards. It does not learn features from pixels or choose behavior policies.