# Paper Summary - Hierarchical and Interpretable Skill Acquisition in Multi-Task Reinforcement Learning by Shu, Xiong & Socher (2017)

Shu, T., Xiong, C., & Socher, R. (2017). Hierarchical and interpretable skill acquisition in multi-task reinforcement learning. arXiv preprint arXiv:1712.07294.

## Paper Summary

This paper presents a technique to perform hierarchical reinforcement learning. It presents a method to train a policy to use previously learned skills to learn more complex skills. The skills can be interpreted in natural language. The authors use a custom Minecraft environment built using Project Malmo as their testbed. They conduct an ablation study using learning curves to demonstrate the impact of their algorithm choices. They compare their hierarchical policy with a “flat” policy to demonstrate its generalizability. They demonstrate its interpretability by displaying the hierarchical plan for several tasks in a tree-based format.

## Methodology

The method presented in the paper trains a policy which learns to solve tasks. Tasks (denoted by $g$) are “skills” which the agent can learn, and each has its associated reward function $R(s, g)$. In the paper, tasks are constrained to a specific template $\langle \text{skill}, \text{item} \rangle$ e.g., $\langle \text{find}, \text{blue} \rangle$ which denote object manipulation tasks. Each task can thus be represented in natural language.

The model is trained to solve tasks in a hierarchical fashion. It first learns to solve “base” level tasks using the environment action set. The task set is then augmented with “higher-order” tasks which can ostensibly be solved using the lower-order task policies, and a “higher-order” policy is trained on this new task set, which constrains it to use as “actions” the tasks from the lower-order policy. This process is repeated until all tasks have been learned. Figure 1 in the paper shows how the task “stack blue” is learned by composing the lower-order tasks “get blue”, “find blue” and “put blue”.

Concretely, the model defines the global policy of a level in the hierarchy (denoted by $\pi_k$, with $k$ being the level) using the following sub-policies,

1. base policy: the global policy of the previous level i.e., $\pi_{k-1}$
2. instruction policy: informs the base policy which base task it needs to execute; defined using conditionally independent distributions for $\text{skill}$ and $\text{item}$ ($\pi_k^{\text{instr}}(g’|s_t,g)$)
3. augmented flat policy: allows selection of base actions at any level to ensure that the global policy is able to perform novel tasks that cannot be achieved by reusing the base policy ($\pi_k^{\text{aug}}(a|s_t, g)$)
4. switch policy: determine whether to use the base policy or the augmented flat policy $\pi_k^{\text{sw}}(e_t|s_t,g)$ where $e_t$ is a binary variable where $0$ selects the base policy, and $1$ selects the augmented policy

The global policy $\pi_k(a_t|s_t,g)$ can thus be denoted compactly as -

$e_t \sim \pi_k^{\text{sw}}(e_t|s,g) \tag{switch policy}$ $g_t' \sim \pi_k^{\text{instr}} (g'_t|s_t,g) \tag{instruction policy}$ $a_t \sim \pi_k(a_t|s_t,g) = \pi_{k-1}(a_t|s_t,g')^{(1-e_t)}\pi_{k}^{\text{aug}}(a_t|s_t,g) \tag{global policy}$

The global policy is augmented with the use of an STG (spatial temporal grammar) to capture temporal relationships between tasks. If a particular order of task selection has been used in the past, the STG will be able to provide it as a prior to the other policies. Concretely, the STG learns the distribution of an alternate Markov chain from the sequence of $\langle e_t,g_t’ \rangle$ tuples conditioned on a specific task. giving us the transition probabilities $\rho_k(e_t,g_t’|e_{t-1},g_{t-1}’,g)$ and the distribution of $\langle e_0,g_0’ \rangle$ as $q_k(e_0,g_0’|g)$. These are used to augment the switch and instruction policies of the respective level.

Learning this policy proceeds in two phases. First, tasks are learned only by sampling tasks from the previous task set, ensuring that the global policy learns to connect tasks to previously learned tasks. In the next phase, it is allowed to sample the full action set, allowing it to discover new ways to complete tasks.

All policies are optimized using advantage actor-critic (A2C). The advantage functions used are provided in the paper. Other training details to stabilize learning and increase episode efficiency are also provided. The STG is trained using simple MLE.

## Experimental Setup

The authors use a custom room in Minecraft built using the Malmo platform as their environment. They define the tasks as “find X”, “get X”, “put X” and “stack X” with 6 different block colours, amounting to 24 different tasks. Each task has its own reward function also defined.

The authors adopt a specific skill acquisition order but stress than any alternate order would not invalidate the conclusions.

The authors perform an ablation study with different versions of their model without certain features and a baseline flat policy. They plot the learning curves for each of these models to compare average reward gained and convergence rates. They also demonstrate the efficacy of their 2-phase curriculum learning using this method.

The authors compare the performance of their policy vs. a flat policy trained on the first level of tasks (i.e., “get X”). They use two rooms with differing number of objects for this.

Lastly, the authors present a visualization of the plans of several tasks generated by their policy. They use it to claim interpretability.

## Results and Analysis

The ablation study confirms that the algorithm and training choices do indeed provide higher reward compared to the flat policy and improve convergence rate. Their policy far outperforms the flat policy, demonstrating the generalization capability of the model.

## Discussion

The authors admit the reliance on “weak human supervision” to define the order of skills to be learned in each training stage, with future work involving how to increase the task set automatically.

## Impressions

This work is situated more in hierarchical RL than in XRL. The “explanations” or interpretability of the policy was very briefly touched on in the paper, and the bulk of the focus was more on demonstrating performance improvement. Regarding interpretability, it does seem like a good tool for showing the hierarchy of the learned policy. However, I question whether a domain will have tasks which neatly fit the $\langle \text{skill}, \text{item} \rangle$ template used here, or whether the tasks will have a sensible hierarchy among them. We might have the policy learn a hierarchy for tasks which make no sense to a human (which isn’t a bad thing, since it helps debug the system).

I’m not very familiar with the field of hierarchical RL. It seems like a major authoring burden to define a set of useful tasks, and an appropriate hierarchy of them for learning. The tasks need to be composed in terms of the base action sets, and, if we want interpretability, need to be translated for humans.

Regarding changing the order of the task sets, the authors simply mention -

One may also alter the order, and the main conclusions shall still hold.

I would have liked to see the effects of reversing the order used in the paper on training and performance.

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