GAE

Learning objectives Implement Generalized Advantage Estimation (GAE): compute advantage estimates \(\hat{A}_t\) from a trajectory of rewards and value estimates using \(\gamma\) and \(\lambda\). Write the recurrence: \(\hat{A}t = \delta_t + (\gamma\lambda) \delta{t+1} + (\gamma\lambda)^2 \delta_{t+2} + \cdots\) where \(\delta_t = r_t + \gamma V(s_{t+1}) - V(s_t)\). Use GAE in a PPO (or actor-critic) pipeline so advantages are fed into the policy loss. Concept and real-world RL GAE (Generalized Advantage Estimation) provides a bias–variance trade-off for the advantage: \(\hat{A}t^{GAE} = \sum{l=0}^{\infty} (\gamma\lambda)^l \delta_{t+l}\). When \(\lambda=0\), \(\hat{A}_t = \delta_t\) (1-step TD, low variance, high bias). When \(\lambda=1\), \(\hat{A}_t = G_t - V(s_t)\) (Monte Carlo, high variance, low bias). Tuning \(\lambda\) (e.g. 0.95–0.99) balances the two. In robot control and game AI, GAE is the standard way to compute advantages for PPO and actor-critic; it is implemented with a backward loop over the trajectory. ...

Learning objectives Implement a full PPO agent for LunarLanderContinuous-v2: policy (actor) and value (critic) networks, rollout buffer, GAE for advantages, and multiple epochs of minibatch updates per rollout. Tune key hyperparameters (learning rate, clip \(\epsilon\), GAE \(\lambda\), batch size, number of epochs) to achieve successful landings. Relate each component (clip, GAE, value loss, entropy bonus) to stability and sample efficiency. Concept and real-world RL PPO in practice: collect a rollout of transitions (e.g. 2048 steps), compute GAE advantages, then perform several epochs of minibatch updates on the same data (policy loss with clip + value loss + entropy bonus). The rollout buffer stores states, actions, rewards, log-probs, and values; after each rollout we compute advantages and then iterate over minibatches. LunarLanderContinuous is a 2D landing task with continuous thrust; it is a standard testbed for PPO. In robot control and game AI, this “collect rollout → multiple PPO epochs” loop is the core of most on-policy algorithms. ...