Direct Explanation
TD(0) and TD(λ) are temporal difference (TD) learning algorithms used to estimate value functions in reinforcement learning. TD(0) updates the value of a state based on the immediate reward and the estimated value of the next state. For example, if an agent transitions from state S to S' and receives reward R, TD(0) adjusts S's value toward R + γV(S'), where γ is a discount factor. This is a one-step update, meaning it only considers the next state. In contrast, TD(λ) introduces a parameter λ (between 0 and 1) to blend multiple future steps into the update. When λ=0, TD(λ) behaves exactly like TD(0), but with λ>0, it aggregates rewards and values over a longer horizon, weighted by how far they are from the current state.
Mechanics of Eligibility Traces
The key difference lies in how TD(λ) uses eligibility traces to track the influence of past states. An eligibility trace assigns a “credit” to states based on their recent activity. For instance, if an agent moves through states S1 → S2 → S3 and receives a reward at S3, TD(λ) propagates updates backward to S2 and S1 using decaying weights. The trace for each state is updated by γλ at each step, meaning older states receive less credit. This allows TD(λ) to handle delayed rewards more effectively than TD(0). For example, in a game where a reward occurs after a sequence of actions, TD(λ) updates all relevant states in the path, while TD(0) only updates the state immediately preceding the reward.
Practical Considerations
TD(0) is simpler computationally, as it avoids storing eligibility traces and performs updates in constant time per step. This makes it suitable for environments with frequent, immediate rewards. However, TD(λ) is more efficient in sparse or delayed reward scenarios (e.g., a robot learning to navigate a maze where rewards come at the end). The trade-off is increased memory and computation, as eligibility traces must be maintained for all states. Developers might choose TD(0) for simplicity or real-time systems, while TD(λ) is preferable when rewards are infrequent and long-term credit assignment is critical. The choice of λ allows tuning between short-term (TD(0)-like) and long-term (closer to Monte Carlo) updates.