Playing Atari Ball Games with Hierarchical Reinforcement Learning

09/27/2019 ∙ by Hua Huang, et al. ∙ Florida State University 0

Human beings are particularly good at reasoning and inference from just a few examples. When facing new tasks, humans will leverage knowledge and skills learned before, and quickly integrate them with the new task. In addition to learning by experimentation, human also learn socio-culturally through instructions and learning by example. In this way humans can learn much faster compared with most current artificial intelligence algorithms in many tasks. In this paper, we test the idea of speeding up machine learning through social learning. We argue that in solving real-world problems, especially when the task is designed by humans, and/or for humans, there are typically instructions from user manuals and/or human experts which give guidelines on how to better accomplish the tasks. We argue that these instructions have tremendous value in designing a reinforcement learning system which can learn in human fashion, and we test the idea by playing the Atari games Tennis and Pong. We experimentally demonstrate that the instructions provide key information about the task, which can be used to decompose the learning task into sub-systems and construct options for the temporally extended planning, and dramatically accelerate the learning process.

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1 Introduction

Humans are especially capable in solving new tasks by leveraging prior knowledge acquired by years-long interaction with the real-world, receiving systematic education, and learning from others. Humans are also particularly good at building rich internal models, which in practice are approximate but sufficiently accurate to guide inference and prediction[11]. When humans face a new task, like learning to drive a car or playing a new video game, they do not start the new task from scratch. For example, when one learns how to drive, first of all one needs to go a thorough traffic rule learning phase and in most cases take a traffic rule test, before any driving is done. To prepare for the test, one needs to read the drivers’ license handbook, in which there are introductions about traffic controls such as pavement markings and traffic control signals. Once one passes the traffic rule test and obtains the learner’s permit, he/she is equipped with the theoretical knowledge for driving and can start to build and sharpen his/her skills by driving a car on road. Furthermore, in the actual driving, one does not learn to drive from scratch, but instead uses the knowledge and skills built while growing up to assist the task. For example, when learning to drive, most of us already know Newtonian physics, basic mathematics and how to understand the world around us using our vision. Based on the acquired skill set, we build a generative model for the entities involved in driving. For example, we have a qualitative understanding of the dynamics of the car, and we can guess the intentions of other drivers and pedestrians to act correspondingly. These rich models dramatically accelerate the learning process. Moreover, it is typically required by law that a new driver carrying a learner’s permit be accompanied by a licensed driver in the front passenger seat while he or she is driving on the road. Thus most drivers learn to drive with an experienced driver providing guidance, and some even go to driving school, where professional teachers teach students how to drive. When taught by a human, hundreds of concrete and/or abstract concepts are injected into the student, which can be then leveraged to quickly grasp the key structures of driving. By actually driving a car on the road, students reinforce their understanding of these instructions. First-hand driving experience gradually gives them information on the response of the car when different actions are taken in diverse driving scenarios. With more practice, the learner becomes more and more experienced and is finally able to drive smoothly. Typically after less than 20 hours of driving, one is ready to go anywhere in any car under any weather conditions.

Another example of learning with guidance is playing video games. Most of new players will first of all take a look at the user manual. This manual will usually contain a basic introduction to the game environment, the rules of playing the games, the hints on how to play it well, and even more, there might be a specially designed game mode in which the game speed is lower, so the player can learn how to manipulate their agent in an easier and more friendly game environment. Once the player got a feeling of the game and built the basic necessary skills, they can switch to the normal game environment and further sharpen their game playing skills. It’s also quite common that humans will begin learning by watching videos of professional games playing played by experts. By mimicking the expert behavior, the gamer can quickly pickup the tactics of playing the game.

Based on these observations, we argue that in real world tasks, which are either designed by humans, and/or for humans, very likely there exist "user manual" -like materials to begin with, and experts to learn from. There types of guidance typically provide essential information about the environment that humans are going to interact with, the rules to follow, and what’s more important, the guidance and hints on how to accomplish the designated task. Based on these hints, we can constrain our choices and build a roadmap to accomplish the task, which reduces the search space dramatically, especially when the dimension of environment is high and the task involves many decision making steps. In this work, we will focus on the guidance and/or hints, and apply them within the framework of hierarchical reinforcement learning. Hierarchical reinforcement learning may be one of the most promising approaches if we want to use reinforcement learning to solve real-world applications, which typically have sparse rewards and long decision processes.

2 Related Work

Hierarchical reinforcement learning has been long considered appealing for solving problems that have long decision processes in complex environments. The learning system has to learn to represent spatial-temporal abstractions and explore environment efficiently. The traditional

-greedy policy works well for local exploration but behaves poorly when the optimal policy involves extended state-action sequences. Typically the goal in hierarchical reinforcement learning is to decompose the task into subtasks that are easier to solve. Another consideration in taking a hierarchical approach is that the world operates in a combinatorial way, and even better, in many cases we can find the entities involved obey a relatively simple law. We can adopt a divide-and-conquer approach and use an appropriate approach for learning the subtask, which could be an analytical approach, a supervised learning or even an unsupervised learning approach, model-based or model-free. Each approach has its strengths and weaknesses, and we can choose the appropriate one to tackle the sub-system.

Most of the current efforts in hierarchical reinforcement learning are focused on automatically learning the options, which are the higher level actions. Bacon at al. [1] proposed to learn options end-to-end automatically. Since the optimal policy is carried out by primitive actions, we theoretically do not need temporally-extended options. Correspondingly, their policies converged to either one single long option or trivial options that last only one step. They had to add regularization to the reward signal to encourage temporally extended options. Another limitation in their work is that they assume the options apply everywhere. The learned options can be difficult to interpret and have no semantic meanings. Riemer et al. [18] extended the automatic option learning to arbitrary deep hierarchies from two abstraction levels, and experimentally demonstrated that for significantly complex problems, more than two levels of abstraction can be beneficial for learning. Machado et al. [13] addressed the option discovery problem by showing how Proto-value functions (PVFs) implicitly define options. PVFs capture the large-scale geometry of the environment, and options based on them can better explore the state space. When the number of states is large, and/or we cannot populate the intermediate and/or final states, which is typical in many of the real-world examples we are interested in, it will be challenging to calculate the PVFs.

Roderick et al. [19] extend the abstraction concept to the state space. The authors argued that in many real world situations, there are natural decompositions of the low-level state into abstract components. Expert like human can provide the abstraction of the state space, and the high-level abstract states can be used as goals for lower-level agents. This state-level abstraction enhanced the exploration for long-term planning.

Another direction related to our work is to learn a set of basic skills by pre-training, and build a high-level policy based on these skills. Florensa et al. [4] proposed to learn the basic skills by pre-training, in which prior knowledge about what high level behaviors might be useful in the subsequent tasks are encoded in the rewards for the pre-training tasks. Once these skills are learned, the top-level policy is trained to select these skills to accomplish the major task. Riedmiller et al. [17] suggested that just like humans have a playful phase of childhood, in which infants interact with environments and learn basic skills like touching and moving objects, and eventually build higher level skills, one can reward the agent to explore the entities and learn basic skills when the outside reward is sparse.

There are also works that focus on designing the reward and/or goals when the outside reward is sparse and hence difficult to learn. Nachum et al. [16] designed a two-level policy, where the high-level policy produces goals indicating desired changes in the state observations, and the lower-level policy chooses actions to reach these specific states. However, this design is limited to applications where we already know the target goal state, for example, robots for the locomotion task. Kulkarni et al. [10] proposed to use an intrinsic reward to accelerate learning. In their experiments of playing video games, an intrinsic reward is defined as the agent reaches different objects, and eventually the agent learns the interplay between the entities of the system as options. Jaderberg et al. [8] demonstrated that changes of pixel values in the input frames or the learned features in the hidden layers can be treated as pseudo-rewards and accelerate the learning when the external reward is sparse. Vezhnevets et al. [23] introduced FeUdal Networks, which is an extension of the work by Dayan et al. [3]. In this architecture, the manager learns to set sub-goals as directions in the latent state space, and the worker learns to fulfill the goals, which can be done using a mixture of internal and external rewards.

Harb et al. [5] formulate what good options should be in the bounded rationality framework. Since absolute optimality is achieved by primitive actions, options are not necessary if we only focus on achieving optimal final performance. The rational of designing temporal abstraction is that it can facilitate the learning and achieve a better balance of learning speed and final performance.

There are some closely related methods to our work. Tsividis et al.[22] investigated human learning in Atari. They experimentally demonstrated that when humans read the game’s original instruction manual prior to playing, the first-episode mean score in the game Frostbite increases from 356 to 1848. They demonstrated that the instruction manual helps humans to form a model-like representation of the game and enable rapid learning. Le et al. [12]

imported expert guidance by imitation learning to pick the subtasks and their rewards at the coarse (higher) level, and the agent carried out the reinforcement learning to accomplish the assigned subtask in the fine (lower) level. Mahjourian et al.

[14] played robot table tennis using a hierarchical control framework. The learning task is decomposed to a model-free reinforcement learning, a model-based prediction of ball trajectory, and analytical controllers of the robot. This strategic decomposition takes advantage of the strengths of these different approaches. The training and debugging are also more manageable when only one skill is in focus on at a time. Designing a real-world robot table tennis is very challenge, and in this work, after 2 million episodes of cooperative games against itself, the best policy can only return the ball about twice, namely the first robot could not return the ball after the second robot hit it.

3 Hierarchy from instructions

The automatic discovery of options that can accelerate the learning and yet not impose too many constrains to severely jeopardize the final performance, is one of the hardest problems in AI research [6]. Current main approaches use deep reinforcement learning trained end-to-end, in which typically pixel values are fed in, and end policies are output. This approach is extremely data thirsty and unnatural to humans. For example, DQN [15] was trained on 200 million frames for each of the games, which equates to approximately 924 hours of game time (about 38 days), or almost 500 times as much experience as the human received. The flexibility of the end-to-end approach might seems appealing at first, but the computation expense is extremely high. This approach is also unnatural to human learning. For example, it’s very unlikely that we let a beginner drive a car on the road alone to learn how to drive, and expect the learner to learn to drive proficiently after many hours of trial- and-error search, during which the learner has to run over pedestrians many times to learn the policy of not hitting a pedestrian.

Most of the tasks human faced are accompanied by some form of documentation. This documentation typically provides an introduction to the basics of the environment, objects and targets, rules, and most importantly, a set of instructions of how to accomplish the task. The perfect example is video game playing, in which a user manual is expected to be included. In this work, we decompose the task based on this documentation, and focus on constructing the options based on the instructions.

In this work, we experimented the idea with the user manual for the Atari video game of Tennis and Pong. The reason we pick these two game is threefold. First of all, the entities in this game are just three, namely agent, tennis, and opponent. The interactions and relationships between these three can be modeled using a linear model, which will simplify our analysis. Second, they are challenging games to play. The state-of-the-art result for Tennis achieves 23.6 after 200 million frames, while most other deep approaches rarely achieve above zero score, namely they cannot beat the embedded AI[7]. Third, they have a good analogy with playing ball games in the real world. Professional tennis player will learn to play tennis under the guidance of coaches, and coaches play a key role in sharpening the learner’ skills.

Description Interpretation

Moving the joystick left moves your player left, moving it right moves him right.

Action effect.

When you’re volleying at the net, your shots don’t travel as far as they do when you hit them from the baseline. you’ll be able to hit your most sharply-angled shots while playing at the net.

Distance to the net determines hit effect.

Aim and "place" the ball depending on how you hit it. The angle of your shot is controlled by where you hit the ball on your racket. If you hit the ball in the center of the racket, your shot will go straight forward. The closer you hit the ball to the edge of the racket, the sharper the angle will be in the direction your racket is facing. Aim your shots and hit them out of reach of your opponent.

The angle of shots is controlled by where you hit the ball on your racket: hit the ball in the center of racket, go straight, hit the ball to the edge of racket, the angle will be sharp.

Once you understand the game’s basics, we suggest you start off with game 3 or 4 and play in slow motion for a while. Put the difficulty switches in the b (down) position. You’ll soon get the feeling of the court, when to rush the net, when to lay back and play the baseline.

Understand basics first, practice with easy motions second, and learn higher-level tactics last.

Hit a sharply-angled serve off the edge of your racket to either the right or left side, then move quickly about two-thirds of the way to the net.

Switch from hit to wait motion.

Table 1: Key instructions from the Atari game Tennis user manual that are relevant for the proposed hierarchical approach

3.1 Hierarchy in ATARI video game Tennis

The original accompanying manual for the Atari video game Tennis can be found at https://atariage.com/manual_html_page.php?SoftwareLabelID=555.

The key instructions relevant for hierarchy are listed in Table 1. These instructions are of tremendous values to build a machine learning system to play the game Tennis, especially if we want the agent to learn in a human-like fashion.

  • Action effect, which indicates we can build lower-level skills to move the agent. These can be done using supervised learning, reinforcement learning or even analytically.

  • The key features in the game planning is that only the hit position matters. First, distance to the net determines the hit effect of how long will the ball travel and how sharp-angled will the shot be. The shot angle is also controlled by how close the ball is hit relative to the center of the racket.

  • The top-level policy (strategy) of the game becomes deciding when to rush the net, when to play the baseline, and how large the shot angle should be.

  • The game can be decomposed naturally into two motions, hit and wait.

Following these instructions, the movement skills are pre-trained first as basic skills offline, a set of options are designed based on the hit location (specified by distance to the net and distance of the hit point to the center of the racket). A hierarchical reinforcement learning policy is eventually trained to chain these options together to play the game.

3.2 Hierarchy in ATARI video game Pong

The accompanying manual can be found at https://boingboing.net/2015/11/07/read-the-manual-to-pong-1976.html. Similar to the settings in the game Tennis, in Pong only the hit position matters. The game task can be naturally decomposed to predict the ball trajectory and the movement of the paddle. Again, these prediction models can be pre-trained offline.

4 Model and Algorithm

4.1 Preliminaries

Reinforcement learning can be formalized as a Markov Decision Process (MDP), which can be denoted as a tuple

, where is set of states, is set of actions,

is the state transition probability,

is the reward function, and is the discount. Here we consider episodic tasks in a discrete state space and a discrete action space.

Sutton et al. [21] formulated the hierarchical reinforcement learning by introducing the concept of option, which is a generalization of the primitive actions to include temporally extended courses of action. An option consist of three components: intra-option policy , termination condition , and initial set . When options are temporally extended, the decision process becomes a semi-MDP.

In this paper we adopt a call-and-return option execution model [1], in which the agent chooses an option according to a policy over the options , then follows the intra-option policy until the termination condition , and these steps are repeated until an episode is terminated.

4.2 The State-Option-Reward-State-Option() algorithm

Compared with Q-learning, which is more popular in Deep Reinforcement Learning, SARSA is an on-policy method that is stable when combined with bootstrap and a non-linear model. In this work, the SARSA() algorithm from flat reinforcement learning is generalized to a State-Option-Reward-State-Option () algorithm for hierarchical reinforcement learning. Within the hierarchical reinforcement learning framework, option value function is defined as

(1)

where , the composition of and , indicates the semi-MDP policy that first follows option until it terminates and then chooses the next option according to policy over option [21]. The semi-MDP version of Q-learning update is:

(2)

where denotes the number of time steps elapsed between and , and

denotes the cumulative discounted reward over this time interval. When the option values are represented via function approximation parameterized by a weight vector

, it is updated via the update rule

(3)

in which the temporal extended TD error of the state-option value is:

(4)

and the state-option value form of the eligibility trace is:

(5)

in which is trace decay parameter [20].

  
  
  for  to  do
     
      { R is the discounted cumulative reward}
     
     Reset game and get start state
     Choose option with -greedy
     
     while  is not terminal state do
        Execute and obtain next state and reward from environment
        
        
        if  is terminal then
           
           
           
        else if  terminates at  then
           Choose option with -greedy
           
           
           
           
           
           
           
           
        else
           
           
        end if
        Anneal
     end while
  end for
Algorithm 1 SORSO() algorithm

In Algorithm  1, the sub-policy is a pre-trained skill, which will be discussed more in the Experiments Section.

5 Experiments

5.1 Atari game Tennis

Setup

The Atari game Tennis (see Figure  1) is played with both hierarchical and flat policy reinforcement learning. Using the instructions from the handbook, a hierarchical policy and set of options are designed. When the ball starts flying towards the agent, a hit mode is activated. In the hit mode, the option is designed as , in which is the distance between the hit position and the base of the net, and is the difference between the hit position and the center of the racket. These values are discretized to , in which is the half length of the tennis court, and . The values of are chosen such that they cover both ends of the court and intermediate locations between the two ends. The values of

are chosen heuristically and cover the spectrum from dangerously close to the racket edge (which leads to a highly skewed trajectory) to center (which leads to a straight shot).

The wait mode is activated when the agent hits back the ball, and the option moves the agent to two thirds of the way to the net, and the middle between the sidelines. In the wait mode, if the agent has not arrived at the designated location but detects the tennis has been hit back, it will immediately switch to hit mode.

Figure 1: A frame from the game Tennis.

To carry out options, a key observation is that the trajectory of the ball needs to be predicted accurately. In this game design, when the ball is flying, its velocity on the horizontal surface is fixed, so the projection of the ball trajectory on the court is a straight line and we can analytically predict the projection with zero error. Another component is the low-level skill of moving to the designated location. In this game, we always try to move to the target location as soon as possible. The action effect can be pre-trained offline, and in this game design, the movement of one step of action is fixed, so the subpolicy can be derived analytically here.

Training

In this experiment, we used the Gym toolkit [2] as the simulation bed. The positions of objects (namely agent, ball, and opponent) and the ball velocity comprise the system state, and a set of Fourier features [9] are calculated based on this state. The learning rate is set to be , discount ratio , and eligibility trace decay factor . The exploration parameter is decreased exponentially. To make a comparison with the flat reinforcement learning, a flat policy is also trained here with the SARSA()[20] algorithm.

Results

Figure 2: Learning curve for the game Tennis. Each curve is smoothed with a 10-set moving average.

The learning curves are plotted in Figure  2. In hierarchical reinforcement learning, after about 4 million frames, the agent achieved the upper bound of its performance, 24, namely wins all the points in a single set. The agent achieved the human level performance of after about 0.1 million trained frames, while a human player needs about two hours of practice, which amounts to around 0.4 million frames on a 60 Hz emulator[15], to achieve this level of performance. The agent learned to play the game with human-level efficiency and quickly outperforms humans. The hierarchical policy learns an order of magnitude faster than the flat policy. The agent also outperforms an end-to-end deep reinforcement learning system by a large margin with respect to learning efficiency (5 million vs. 200 million frames trained[7]).

5.2 Atari game Pong

Setup

Instructed by the manual, the hit mode and wait mode are designed just as in Tennis. In the hit mode, the option is designed as , and is the difference between the hit position and the center of the agent paddle, . For reference, the height of paddle is 8, and height of the ball is 2, so values of cover all the possible hit positions. When the ball is hit to the opponent, the wait mode is activated and action of no-op is imposed until the ball gets hit back by the opponent. Since the agent can move swiftly, the paddle does not need to be moved to the center in wait mode.

To implement options, a model for the movement of the ball and movement of the paddle has to be built. In this game design, when the ball is flying, the velocity is fixed, so we can predict it precisely. The low-level skill of moving to the designated location is built on the action effects on the paddle, which is pre-trained offline.

Figure 3: A frame from the game Pong.

Training

The same setting as in playing Tennis is adopted here. A predictive model for the action effect is also trained using supervised learning. The past 4 frames of agent paddle and the past 3 actions are recorded to predict the action effect. To collect the samples, a random policy is

Figure 4: Learning curve for the game Pong. Each curve is smoothed with a 10-game moving average.

implemented and 1 million unique samples are collected. After training, a training error of 1.06 is achieved for the action “no-op”, 1.47 for the action “up”, and 1.52 for the action “down”. It’s noteworthy that the predictive model is not perfect. A careful inspection on the samples indicates that the agent paddle moves with significant randomness. Although the predictive model cannot be precise, experiments show that it is adequately reliable for the top-level policy. In this study, the prediction model for the agent movement effect and model for the ball trajectory prediction are constructed explicitly and in isolated manner. In end-to-end reinforcement learning, all these sub-skills are learned together implicitly. With the diverse entities involved and entangled, it will be much more difficult to learn them all at once.

Results

The learning curves are plotted in Figure  4. In hierarchical reinforcement learning, after about 0.6 million frames, the agent achieved human level performance of 9.3[15]

, and a human needs about 0.4 million frames of practicing to achieve this score. The hierarchical policy learns an order of magnitude faster than the flat policy, and got a final performance around 19, while the flat policy got a final performance about 18.3. The hierarchical policy outperforms an end-to-end deep reinforcement learning system in efficiency by an order of magnitude, while the flat policy learns with about the same speed as deep learning.

6 Conclusion

In this work we propose that machines can learn from instructions provided by handbooks and/or expert human, and these instructions can provide hierarchical decomposition of the task into components, which can be tackled by different learning systems to take advantage of their strengths. Instruction manuals also provide an abstract illustration of the key features of the environment, such as guidelines of the spatial-temporal structure of the planing procedure, to accelerate the exploration of the environment. Low-level skills can also be advised by instructions to build supporting models for rapid learning. The experiments indicate that using instructions from handbook, machines can learn as fast as human and reach human-level performance with the same amount of training data, and outperform humans after more training. The building of the supporting models and the appropriateness of the option construction are the two key factors in the learning ability of the hierarchical agent.

References