Short Answer

Validating a Potential-Based Shaping Function

An AI developer is implementing a reward shaping function, f, to guide a reinforcement learning agent. They have defined a potential function, Φ(s), which estimates the value of any given state s, and are using a discount factor γ. They are considering three different formulas for the shaping reward based on a transition from state s_t to s_{t+1}:

  1. f = Φ(s_{t+1}) - Φ(s_t)
  2. f = γΦ(s_{t+1}) - Φ(s_t)
  3. f = Φ(s_{t+1})

Which of these formulas should the developer choose to ensure that the agent's optimal policy is not altered by the additional reward? Justify your choice by explaining why it is correct and why the other two are not.

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Updated 2025-10-08

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