Differentiable Tree Search in Latent State Space

In decision-making problems with limited training data, policy functions approximated using deep neural networks often exhibit suboptimal performance. An alternative approach involves learning a world model from the limited data and determining actions through online search. However, the performance is adversely affected by compounding errors arising from inaccuracies in the learnt world model. While methods like TreeQN have attempted to address these inaccuracies by incorporating algorithmic structural biases into their architectures, the biases they introduce are often weak and insufficient for complex decision-making tasks. In this work, we introduce Differentiable Tree Search (DTS), a novel neural network architecture that significantly strengthens the inductive bias by embedding the algorithmic structure of a best-first online search algorithm. DTS employs a learnt world model to conduct a fully differentiable online search in latent state space. The world model is jointly optimised with the search algorithm, enabling the learning of a robust world model and mitigating the effect of model inaccuracies. We address potential Q-function discontinuities arising from naive incorporation of best-first search by adopting a stochastic tree expansion policy, formulating search tree expansion as a decision-making task, and introducing an effective variance reduction technique for the gradient computation. We evaluate DTS in an offline-RL setting with a limited training data scenario on Procgen games and grid navigation task, and demonstrate that DTS outperforms popular model-free and model-based baselines.