Lambda's Balancing Act

In an actor-critic setup, the critic estimates $V(s)$ , and GAE computes $\hat{A}$ , where $\delta_t = r_t + \gamma V(s_{t+1}) - V(s_t)$ . What happens to the estimator's bias and variance as $\lambda \to 0$ versus $\lambda \to 1$ ?

$\lambda \to 1$ removes both bias and variance simultaneously because it averages over strictly more terms.

$\lambda \to 0$ gives the low-variance, high-bias one-step TD advantage (just $\delta_t$ ); $\lambda \to 1$ gives the high-variance, low-bias Monte Carlo-style advantage estimate as the residuals telescope into the full return.

$\lambda \to 0$ gives the unbiased Monte Carlo return; $\lambda \to 1$ collapses to a single TD residual with lower variance.

$\lambda$ only rescales the discount factor $\gamma$ , so it has no independent effect on bias or variance.