Reinforcement Learning (RL) algorithms often suffer from low training efficiency. A strategy to mitigate this issue is to incorporate a model-based planning algorithm, such as Monte Carlo Tree Search (MCTS) or Value Iteration (VI), into the environmental model. The major limitation of VI is the need to iterate over a large tensor. These still lead to intensive computations. We focus on improving the training efficiency of RL algorithms by improving the efficiency of the value learning process. For the deterministic environments with discrete state and action spaces, a non-branching sequence of transitions moves the agent without deviating from intermediate states, which we call a highway. On such non-branching highways, the value-updating process can be merged as a one-step process instead of iterating the value step-by-step. Based on this observation, we propose a novel graph structure, named highway graph, to model the state transition. Our highway graph compresses the transition model into a concise graph, where edges can represent multiple state transitions to support value propagation across multiple time steps in each iteration. We thus can obtain a more efficient value learning approach by facilitating the VI algorithm on highway graphs. By integrating the highway graph into RL (as a model-based off-policy RL method), the RL training can be remarkably accelerated in the early stages (within 1 million frames). Comparison against various baselines on four categories of environments reveals that our method outperforms both representative and novel model-free and model-based RL algorithms, demonstrating 10 to more than 150 times more efficiency while maintaining an equal or superior expected return, as confirmed by carefully conducted analyses. Moreover, a deep neural network-based agent is trained using the highway graph, resulting in better generalization and lower storage costs.

What is a useful skill hierarchy for an autonomous agent? We propose an answer based on the graphical structure of an agent's interaction with its environment. Our approach uses hierarchical graph partitioning to expose the structure of the graph at varying timescales, producing a skill hierarchy with multiple levels of abstraction. At each level of the hierarchy, skills move the agent between regions of the state space that are well connected within themselves but weakly connected to each other. We illustrate the utility of the proposed skill hierarchy in a wide variety of domains in the context of reinforcement learning.

There is an extensive literature on the complexity of planning, but explicit bounds on time and space complexity are very rare. On the other hand, problems like the constraint satisfaction problem (CSP) have been thoroughly analysed in this respect. We provide a number of upper- and lower-bound results (the latter based on various complexity-theoretic assumptions such as the Exponential Time Hypothesis) for both satisficing and optimal planning. We show that many classes of planning instances exhibit a dichotomy: either they can be solved in polynomial time or they cannot be solved in subexponential time. In many cases, we can even prove closely matching upper and lower bounds. Our results also indicate, analogously to CSPs, the existence of sharp phase transitions. We finally study and discuss the trade-off between time and space. In particular, we show that depth-first search may sometimes be a viable option for planning under severe space constraints.