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Title: Learning Functionally Decomposed Hierarchies for Continuous Navigation Tasks

Paper content:
Solving long-horizon sequential decision making tasks in environments with sparse rewards is a longstanding problem in reinforcement learning (RL) research.
Hierarchical Reinforcement Learning (HRL) has held the promise to enhance the capabilities of RL agents via operation on different levels of temporal abstraction.
Despite the success of recent works in dealing with inherent nonstationarity and sample complexity, it remains difficult to generalize to unseen environments and to transfer different layers of the policy to other agents.
In this paper, we propose a novel HRL architecture, Hierarchical Decompositional Reinforcement Learning (HiDe), which allows decomposition of the hierarchical layers into independent subtasks, yet allows for joint training of all layers in end-to-end manner.
The main insight is to combine a control policy on a lower level with an image-based planning policy on a higher level.
We evaluate our method on various complex continuous control tasks for navigation, demonstrating that generalization across environments and transfer of higher level policies can be achieved.
See videos https://sites.google.com/view/hide-rl
Reinforcement learning (RL) has been succesfully applied to sequential-decision making tasks, such as learning how to play video games in Atari (Mnih et al., 2013) , mastering the game of Go or continuous control in robotics (Lillicrap et al., 2015; Levine et al., 2015; .
However, despite the success of RL agents in learning control policies for myopic tasks, such as reaching a nearby target, they lack the ability to effectively reason over extended horizons.
In this paper, we consider continuous control tasks that require planning over long horizons in navigation environments with sparse rewards.
The task becomes particularly challenging with sparse and delayed rewards since an agent needs to infer which actions caused the reward in a domain where most samples give no signal at all.
Common techniques to mitigate the issue of sparse rewards include learning from demonstrations (Schaal, 1999; Peng et al., 2018) or using enhanced exploration strategies (Bellemare et al., 2016; Pathak et al., 2017; Andrychowicz et al., 2017) .
Hierarchical Reinforcement Learning (HRL) has been proposed in part to solve such tasks.
Typically, a sequential decision making task is split into several simpler subtasks of different temporal and functional abstraction levels (Sutton et al., 1999; Andre & Russell, 2002) .
Although the hierarchies would ideally be learned in parallel, most methods resort to curriculum learning (Frans et al., 2017; Florensa et al., 2017; Bacon et al., 2016; Vezhnevets et al., 2017) .
Recent goal-conditioned hierarchical architectures have successfully trained policies jointly via off-policy learning (Levy et al., 2019; Nachum et al., 2018; .
However, these methods often do not generalize to unseen environments as we show in Section 5.1.
We argue that this is due to a lack of true separation of planning and low-level control across the hierarchy.
In this paper, we consider two main problems, namely functional decomposition of HRL architectures in navigation-based domains and generalization of RL agents to unseen environments (figure 1).
To address these issues, we propose a novel multi-level HRL architecture that enables both functional decomposition and temporal abstraction.
We introduce a 3-level hierarchy that decouples the major roles in a complex navigation task, namely planning and low-level control.
The benefit of a modular design is twofold.
First, layers have access to only task-relevant information for a predefined task, which significantly improves the generalization ability of the overall policy.
Hence, this enables policies learned on a single task to solve randomly configured environments.
Second, Figure 1 : Navigation environments.
The red sphere indicates the goal an agent needs to reach, with the starting point at the opposite end of the maze.
The agent is trained on environment
a).
To test generalization, we use the environments with
b) reversed starting and goal positions,
c) mirrored maze with reversed starting and goal positions and
d) randomly generated mazes.
the planning and control layers are modular and thus allow for composition of cross-agent architectures.
We empirically show that the planning layer of the hierarchy can be transferred successfully to new agents.
During training we provide global environment information only to the planning layer, whereas the full internal state of the agent is only accessible by the control layer.
The actions of the top and middle layers are in the form of displacement in space.
Similarly, the goals of the middle and lowest layers are relative to the current position.
This prevents the policies from overfitting to the global position in an environment and hence encourages generalization to new environments.
In our framework (see figure 2), the planner (i.e., the highest level policy π 2 ) learns to find a trajectory leading the agent to the goal.
Specifically, we learn a value map of the environment by means of a value propagation network (Nardelli et al., 2019) .
To prevent the policy from issuing too ambitious subgoals, an attention network estimates the range of the lower level policy π 0 (i.e., the agent).
This attention mask also ensures that the planning considers the agent performance.
The action of π 2 is the position which maximizes the masked value map, which serves as goal input to the policy π 1 .
The middle layer implements an interface between the upper planner and lower control layer, which refines the coarser subgoals into shorter and reachable targets for the agent.
The middle layer is crucial in functionally decoupling the abstract task of planning (π 2 ) from agent specific continuous control.
The lowest layer learns a control policy π 0 to steer the agent to intermediate goals.
While the policies are functionally decoupled, they are trained together and must learn to cooperate.
In this work, we focus on solving long-horizon tasks with sparse rewards in complex continuous navigation domains.
We first show in a maze environment that generalization causes challenges for state-of-the-art approaches.
We then demonstrate that training with the same environment configuration (i.e., fixed start and goal positions) can generalize to randomly configured environments.
Lastly, we show the benefits of functional decomposition via transfer of individual layers between different agents.
In particular, we train our method with a simple 2DoF ball agent in a maze environment to learn the planning layer which is later used to steer a more complex agent.
The results indicate that the proposed decomposition of policy layers is effective and can generalize to unseen environments.
In summary our main contributions include:
• A novel multi-layer HRL architecture that allows functional decomposition and temporal abstraction for navigation tasks.
• This architecture enables generalization beyond training conditions and environments.
• Functional decomposition that allows transfer of individual layers across different agents.
In this paper, we introduce a novel HRL architecture that can solve complex navigation tasks in 3D-based maze environments.
The architecture consists of a planning layer which learns an explicit value map and is connected with a subgoal refinement layer and a low-level control layer.
The framework can be trained end-to-end.
While training with a fixed starting and goal position, our method is able to generalize to previously unseen settings and environments.
Furthermore, we demonstrate that transfer of planners between different agents can be achieved, enabling us to transfer a planner trained with a simplistic agent such as a ball to a more complex agent such as an ant or humanoid.
In future work, we want to consider integration of a more general planner that is not restricted to navigation-based environments.

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