by Haytham ElFadeel - [email protected]
2024
Unlike behavior cloning, which copies the average demonstration as-is, reinforcement learning aims to reinforce good actions and discourage bad ones. To do that effectively, we need to know which actions were good, which were bad, and which were irrelevant. This essentially is the credit assignment problem (CAP).
Formally:
Given a return signal, assign blame or credit to the right state-action choices that caused it.
The term was coined by Minsky (1961), who observed that "each ultimate success is associated with a vast number of internal decisions" and that identifying which decisions mattered is a fundamental bottleneck. Six decades later, the CAP remains one of the deepest open problems in RL. It is, arguably, the reason we need RL at all: if we could perfectly decompose an outcome into per-action contributions, policy optimization would reduce to supervised learning.
To make a progress we need to understand the problem, the difficulty comes from three types of uncertainty:
When did the decisive action happen?
Depth captures the temporal distance between a consequential action and the reward that eventually reveals its value.
Example. A robot must open a locked door. The trajectory looks like: robot walk to the key location → pick up the key → walk 100 steps to the door → insert the key → receive a reward. The action "pick up the key" was decisive, yet it occurred far before the reward signal. That distance is the depth.
This is hard because the reward signal must propagate backward through a long chain, and this propagation typically degrades. Think of vanishing gradients in backpropagation through time, or the discount factor $γ$ shrinking contributions exponentially. With a discount of $γ = 0.99$ and a delay of 500 steps, the effective credit reaching the decisive action is $0.99^{500} ≈ 0.0066$ — less than 1% of the original signal. Small value or Q-function estimation errors compound when bootstrapped repeatedly over long horizons, further eroding the signal.
Which actions mattered versus which were irrelevant?