Planning and Learning with Adaptive Lookahead

The classical Policy Iteration (PI) algorithm alternates between greedy one-step policy improvement and policy evaluation. Recent literature shows that multi-step lookahead policy improvement leads to a better convergence rate at the expense of increased complexity per iteration. However, prior to running the algorithm, one cannot tell what is the best fixed lookahead horizon. Moreover, per a given run, using a lookahead of horizon larger than one is often wasteful. In this work, we propose for the first time to dynamically adapt the multi-step lookahead horizon as a function of the state and of the value estimate. We devise two PI variants and analyze the trade-off between iteration count and computational complexity per iteration. The first variant takes the desired contraction factor as the objective and minimizes the per-iteration complexity. The second variant takes as input the computational complexity per iteration and minimizes the overall contraction factor. We then devise a corresponding DQN-based algorithm with an adaptive tree search horizon. We also include a novel enhancement for on-policy learning: per-depth value function estimator. Lastly, we demonstrate the efficacy of our adaptive lookahead method in a maze environment and in Atari.