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Title: Learning Multi-Level Hierarchies with Hindsight

Paper content:
Hierarchical agents have the potential to solve sequential decision making tasks with greater sample efficiency than their non-hierarchical counterparts because hierarchical agents can break down tasks into sets of subtasks that only require short sequences of decisions.
In order to realize this potential of faster learning, hierarchical agents need to be able to learn their multiple levels of policies in parallel so these simpler subproblems can be solved simultaneously.
Yet, learning multiple levels of policies in parallel is hard because it is inherently unstable: changes in a policy at one level of the hierarchy may cause changes in the transition and reward functions at higher levels in the hierarchy, making it difficult to jointly learn multiple levels of policies.
In this paper, we introduce a new Hierarchical Reinforcement Learning (HRL) framework, Hierarchical Actor-Critic (HAC), that can overcome the instability issues that arise when agents try to jointly learn multiple levels of policies.
The main idea behind HAC is to train each level of the hierarchy independently of the lower levels by training each level as if the lower level policies are already optimal.
We demonstrate experimentally in both grid world and simulated robotics domains that our approach can significantly accelerate learning relative to other non-hierarchical and hierarchical methods.
Indeed, our framework is the first to successfully learn 3-level hierarchies in parallel in tasks with continuous state and action spaces.
Hierarchy has the potential to accelerate learning in sequential decision making tasks because hierarchical agents can decompose problems into smaller subproblems.
In order to take advantage of these shorter horizon subproblems and realize the potential of HRL, an HRL algorithm must be able to learn the multiple levels within the hierarchy in parallel.
That is, at the same time one level in the hierarchy is learning the sequence of subtasks needed to solve a task, the level below should be learning the sequence of shorter time scale actions needed to solve each subtask.
Yet the existing HRL algorithms that are capable of automatically learning hierarchies in continuous domains BID11 BID4 BID1 BID15 BID9 do not efficiently learn the multiple levels within the hierarchy in parallel.
Instead, these algorithms often resort to learning the hierarchy one level at a time in a bottom-up fashion.Learning multiple levels of policies in parallel is challenging due to non-stationary state transition functions.
In nested, multi-level hierarchies, the transition function for any level above the ground level depends on the current policies below that level.
For instance, in a 2-level hierarchy, the Figure 1: An ant agent uses a 3-level hierarchy to traverse though rooms to reach its goal, represented by the yellow cube.
Π 2 uses as input the current state (joint positions θ and velocitiesθ) and goal state (yellow box) and outputs a subgoal state (green box) for Π 1 to achieve.
Π 1 takes in the current state and its goal state (green box) and outputs a subgoal state (purple box) for Π 0 to achieve.
Π 0 takes in the current state and goal state (purple box) and outputs a vector of joint torques.high-level policy may output a subgoal state for the low level to achieve, and the state to which this subgoal state leads will depend on the current low-level policy.
When all policies within the hierarchy are trained simultaneously, the transition function at each level above ground level will continue to change as long as the policies below that level continue to be updated.
In this setting of non-stationary transition functions, RL will likely struggle to learn the above ground level policies in the hierarchy because in order for RL methods to effectively value actions, the distribution of states to which those actions lead should be stable.
However, learning multiple policies in parallel is still possible because the transition function for each level above ground level will stabilize once all lower level policies have converged to optimal or near optimal policies.
Thus, RL can be used to learn all policies in parallel if each level above ground level had a way to simulate a transition function that uses the optimal versions of lower level policies.
Our framework is able to simulate a transition function that uses an optimal lower level policy hierarchy and thus can learn multiple levels of policies in parallel.We introduce a new HRL framework, Hierarchical Actor-Critic (HAC), that can significantly accelerate learning by enabling hierarchical agents to jointly learn a hierarchy of policies.
Our framework is primarily comprised of two components:
(i) a particular hierarchical architecture and
(ii) a method for learning the multiple levels of policies in parallel given sparse rewards.The hierarchies produced by HAC have a specific architecture consisting of a set of nested, goalconditioned policies that use the state space as the mechanism for breaking down a task into subtasks.
The hierarchy of nested policies works as follows.
The highest level policy takes as input the current state and goal state provided by the task and outputs a subgoal state.
This state is used as the goal state for the policy at the next level down.
The policy at that level takes as input the current state and the goal state provided by the level above and outputs its own subgoal state for the next level below to achieve.
This process continues until the lowest level is reached.
The lowest level then takes as input the current state and the goal state provided by the level above and outputs a primitive action.
Further, each level has a certain number of attempts to achieve its goal state.
When the level either runs out of attempts or achieves its goal state, execution at that level ceases and the level above outputs another subgoal.
Figure 1 shows how an ant agent trained with HAC uses its 3-level policy hierarchy (π 2 , π 1 , π 0 ) to move through rooms to reach its goal.
At the beginning of the episode, the ant's highest level policy, π 2 , takes as input the current state, which in this case is a vector containing the ant's joint positions and velocities ([θ,θ] ), and its goal state, represented by the yellow box.
π 2 then outputs a subgoal state, represented by the green box, for π 1 to achieve.
π 1 takes as input the current state and its goal state represented by the green box and outputs the subgoal state represented by the purple box.
Finally, π 0 takes as input the current state and the goal state represented by purple box and outputs a primitive action, which in this case is a vector of joint torques.
π 0 has a fixed number of attempts to move to the purple box before π 1 outputs another subgoal state.
Similarly, π 1 has a fixed number of subgoal states that it can output to try to move the agent to the green box before π 2 outputs another subgoal.In addition, HAC enables agents to learn multiple policies in parallel using only sparse reward functions as a result of two types of hindsight transitions.
Hindsight action transitions help agents learn multiple levels of policies simultaneously by training each subgoal policy with respect to a transition function that simulates the optimal lower level policy hierarchy.
Hindsight action transitions are implemented by using the subgoal state achieved in hindsight instead of the original subgoal state as the action component in the transition.
For instance, when a subgoal level proposes subgoal state A, but the next level policy is unsuccessful and the agent ends in state B after a certain number of attempts, the subgoal level receives a transition in which the state B is the action component, not state A. The key outcome is that now the action and next state components in the transition are the same, as if the optimal lower level policy hierarchy had been used to achieve subgoal state B.Training with respect to a transition function that uses the optimal lower level policy hierarchy is critical to learning multiple policies in parallel, because the subgoal policies can be learned independently of the changing lower level policies.
With hindsight action transitions, a subgoal level can focus on learning the sequences of subgoal states that can reach a goal state, while the lower level policies focus on learning the sequences of actions to achieve those subgoal states.
The second type of hindsight transition, hindsight goal transitions, helps each level learn a goal-conditioned policy in sparse reward tasks by extending the idea of Hindsight Experience Replay BID0 ) to the hierarchical setting.
In these transitions, one of the states achieved in hindsight is used as the goal state in the transition instead of the original goal state.We evaluated our approach on both grid world tasks and more complex simulated robotics environments.
For each task, we evaluated agents with 1, 2, and 3 levels of hierarchy.
In all tasks, agents using multiple levels of hierarchy substantially outperformed agents that learned a single policy.
Further, in all tasks, agents using 3 levels of hierarchy outperformed agents using 2 levels of hierarchy.
Indeed, our framework is the first to show empirically that it can jointly learn 3-level hierarchical policies in tasks with continuous state and action spaces.
In addition, our approach outperformed another leading HRL algorithm, HIRO BID9 , on three simulated robotics tasks.
Hierarchy has the potential to accelerate learning but in order to realize this potential, hierarchical agents need to be able to learn their multiple levels of policies in parallel.
We present a new HRL framework that can efficiently learn multiple levels of policies simultaneously.
HAC can overcome the instability issues that arise when agents try to learn to make decisions at multiple time scales because the framework trains each level of the hierarchy as if the lower levels are already optimal.
Our results in several discrete and continuous domains, which include the first 3-level agents in tasks with continuous state and action spaces, confirm that HAC can significantly improve sample efficiency.ONR through N000141410047, Amazon through an ARA to Platt, Google through a FRA to Platt, and DARPA.
• Key agent parameters: number of levels in hierarchy k, maximum subgoal horizon H, and subgoal testing frequency λ.
Output:• k trained actor and critic functions π 0 , ..., DISPLAYFORM0 Sample initial state and task goal DISPLAYFORM1 Begin training Update all actor and critic networks end for function TRAIN-LEVEL(i :: level, s :: state, g :: goal) s i ← s, g i ← g Set current state and goal for level i for H attempts or until g n , i ≤ n < k achieved do DISPLAYFORM2 DISPLAYFORM3 Replace original action with action executed in hindsight end ifEvaluate executed action on current goal and hindsight goals DISPLAYFORM4 Replay Buf f er i ← Perform HER using HER Storage i transitions return s iOutput current state end function

assistant: text: We introduce the first Hierarchical RL approach to successfully learn 3-level hierarchies in parallel in tasks with continuous state and action spaces.