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2 Things You Need to Know about Reinforcement Learning – Computational Efficiency and Sample Efficiency


Experimenting with different strategies for a reinforcement learning model is crucial to discovering the best approach for your application. However, where you land can have significant impact on your system's energy consumption that could cause you to think again about the efficiency of your computations.



The High Cost of Deep Learning

 

Have you ever put on a sweater because the air conditioning was too cold? Forgotten to turn off the lights in another room before heading to bed? Do you commute to work more than 30 minutes every day just for the sake of “filling seats” at the office, even though everything you do at work could be done via laptop from home?

In the counter-intuitive trade-offs between sample and computational efficiency in Reinforcement Learning, choosing evolution strategies can be smarter than it looks.

Modern life is full of inefficiencies small and large, but the energy costs of our deep learning research/passion/enterprise are not so immediately obvious. With a high-powered workstation tower at your desk, the stream of hot air blown out by cooling fans is a constant reminder of the persistence and scale of energy being used. But, if you’re sending jobs to a shared cluster down the hall, it’s a little more difficult to intuitively appreciate the impact of your design decisions on your electricity bill. If you use cloud computing for big jobs, the energy use and pursuant consequences are even more abstracted away from your immediate attention. But out-of-sight, out-of-mind is not a viable policy for making decisions about projects that might, at the extreme end of the scale, may represent a greater energy expenditure than the entire product cycle of an automobile.

 

Energy Requirements for Training Deep Learning Models

 

Strubell et al. brought attention to the substantial energy requirements of training modern deep learning models in 2019. Although they focused mainly on a large type of natural language processing model called a transformer, the considerations and conclusions discussed in their paper should hold roughly true for training deep models for other tasks on similar hardware for about the same amount of time.

They estimated training the large variant of Vaswani et al.’s transformer from scratch emits about 10% of the carbon dioxide equivalent emissions as a flight from New York to San Francisco, based on some assumptions about the energy mix published by major cloud providers, and a financial cost of just less than 1000 USD (assuming cloud compute). For a business-defining project, that’s probably a worthwhile expenditure, but when tuning and experimentation are taken into account, the energy bill can easily be multiplied by a factor of 10 or more.

Strubell and colleagues estimated that adding Neural Architecture Search (NAS) to NLP model development comes with a price tag in the millions and a carbon footprint to match. Although many of the largest models take advantage of dedicated hardware, like Google’s TPUs, to train, and that may decrease the energy costs by 30 to 80X and the price of training by a slightly lower factor, but that’s still a substantial cost. In the realm of reinforcement learning that we are concerned with in this article, the consequences of inefficient training can be a dead project, product, or business.

 

DeepMind Training Example Using Starcraft II

 

Over a period of 44 days, Deepmind trained agents to achieve grandmaster status in all three playable races in the multiplayer real-time strategy game Starcraft II, beating out 99.8% of all players in the Battle.net rankings. OpenAI’s major game-mastery project for Dota 2 employed 10 real-time months (about 800 petaflop/days) of training time to defeat world champion, human players.

Due to the use of TPUs, virtual workers, etc., it’s not easy to accurately estimate the energy costs for such headline-grabbing game players, but estimates fall in the ballpark of a 12 to 18 million USD cloud compute bill to train champion Alphastar and OpenAI Five, respectively. Clearly, that’s out of reach for a typical academic or industry machine learning team. There’s another danger arising from inefficient learning in the field of reinforcement learning. An agent trying to learn a moderately complex task with bad exploration and poor sample efficiency might never find a viable solution.

 

Predicting Protein Structure Using Reinforcement Learning (NL)

 

As an example, we can compare moderately complex reinforcement learning tasks to the challenge of predicting protein structure from a sequence. Consider a small protein consisting of 100 amino acids linked together, like a chain with 100 links. Each link is a specific one out of 21 unique link variants, and the structure will take shape based on the angles between each link in turn. Assuming a simplified 9 possible configurations for the bond angles between each amino acid/chain link, it would take

999 = 29,512,665,430,652,752,148,753,480,226,197,736,314,359, 272,517,043,832,886,063,884,637,676,943,433,478,020,332,709,411,004,889
(that rounds to a 3 followed by 94 zeros) 

iterations to see each possible structure. That 100 link protein is roughly analogous to a reinforcement learning environment with 100 time steps and 9 possible actions at each step. Talk about a combinatorial explosion. 

Of course, a reinforcement learning agent doesn’t set out to randomly sample all possible game states. Instead, an agent will generate learning trajectories through some combination of making their best guess, directed exploration, and random search. But that method of generating experience, typical of what we call “on-policy” learning algorithms, can cut both ways. An agent that finds a local optimum approach to a given reinforcement learning task might just stay there forever, repeating the same mistakes and never solving the overall problem.

Historically reinforcement learning has benefitted from trying to formulate the problem to resemble supervised learning wherever possible, such as sending students hiking with three cameras strapped to their head. The left camera generates an image with a training label to “turn right,” while the right camera is labeled “go left” and the center camera “straight ahead.”

In the end, you would have a labeled dataset suitable for training a quadcopter to navigate forest trails. In the sections below, we’ll discuss how similar concepts (e.g., imitation learning) and model-based RL can vastly decrease the number of training examples necessary for an agent to learn a task and why that is not always a good thing.

 

Doing More with Less: Reinforcement Learning Agents Learn Best from Examples

 

Deep reinforcement learning is a branch of machine learning inspired by fields as diverse as animal and human cognition, optimal control, and deep learning. There are obvious analogs to animal behavior experiments, where an animal (agent) is put in a situation where it must learn to solve a problem to get a food treat (reward). It only takes a few examples before an animal starts to associate a series of actions with a reward, but deep reinforcement learning algorithms may need to consider 10 to 100 thousand time steps per epoch in order to make stable updates to the agent’s parameters.

Most reinforcement learning environments are formulated in steps. The environment generates an observation, based upon which the agent decides an action that is applied to the environment. The environment makes an update based on its current state and the action chosen by the agent in what we refer to as a time step throughout this article. The fewer time steps, or “samples,” needed to learn, the more efficient the algorithm is.

An important aspect of most modern reinforcement learning algorithms is that they are at their core, a form of trial-and-error. For an agent to learn without employing explicit exploration techniques, random activity should occasionally do something right, otherwise, an agent may interact with an environment for (essentially) forever without ever seeing a positive reward. In fact, proximal policy optimization, an algorithm that achieves competitive performance in a range of benchmarks, completely fails in OpenAI’s procedurally generated environment suite in hard exploration mode. We can imagine how this is a problem for a wide range of relevant tasks.

An agent learning to play a video game will probably experience a positive reward with random actions (aka button-mashing), and that is one reason why the Atari suite is a popular reinforcement learning benchmark. For more complex tasks like figuring out how to tie a complex knot, it’s extremely unlikely that a robot will come across a solution by accident. No matter how much random interaction is allowed, arriving at the desired outcome is just too unlikely.

As we’ve seen before in our discussion of learning Rubik’s cube manipulation, there are custom knot tying robots built and programmed manually to create knots, but a reinforcement learning agent that learns to do so from scratch remains out of reach. It goes without saying that humans don’t learn knot-tying from scratch either. A toddler left alone in a room full of untied sneakers will probably have a hard time discovering the standard “bunny rabbit” knot on their own. Like the toddler in the thought experiment, reinforcement learning agents can learn better from examples, even for complicated tasks like making knots.

 

Example of Teaching Machines to Tie Knots Using Reinforcement Learning & More

 

By combining autonomous learning of rope physics with human demonstrations, researchers at Berkeley were able to tackle the problem of teaching machines to tie knots. First, and this part may be simulated, the robot interacts with a rope on a table surface mostly at random, with the intent of learning a reasonable model of how their limited view of the world works. Following the agent’s autonomous learning tenure, it is shown the desired action of tying a simple knot. When all goes well, the agent is able to mimic the desired action. A mix of autonomously learning a dynamics model of the world (in the example above, a table surface with a rope) and human examples of desired behavior is a powerful combination. Imitation learning and the related inverse reinforcement learning represent some of the most sample-efficient approaches to RL out there.

Knot-tying is a slightly esoteric task (and plainly outside the capabilities of many learning algorithms), but we can compare the sample efficiency of different learning algorithms applied to more standard tasks. Lecture 21, slide 39 from Sergey Levine’s deep RL course at Berkeley (pdf), gives us an idea of the relative sample efficiencies for various RL algorithms by comparing published results from the HalfCheetah task. HalfCheetah is a 2D locomotion task for a simulated robot vaguely resembling half a fast feline. Implementations of HalfCheetah are available in both the Mujoco (requires paid license) and Bullet (open source, free) physics simulators.

According to the slide, we expect evolution strategies to be the most sample inefficient and model-based/inverse reinforcement learning to be the most efficient with respect to the total number of time steps. The estimates from the slide are reproduced below, along with specific examples from the literature.

The HalfCheetah robot simulated in PyBullet, where the objective is to move forward as quickly as possible. Although rendered in 3D, movement is constrained to a 2D plane. It’s like a cheetah, but half.

 

Method Estimated steps from CS 285 lec 21 Example time steps to solve HalfCheetah
Evolution strategies ~1,000,000,000 ~3,000,000 (ES, Salimans et al. 2016)
Fully online actor-critic methods ~100,000,000 ~100,000,000 (Trust-A3C, Wang et al. 2016)
Policy gradients ~10,000,000 ~1,000,000 (PPO, Schulman et al. 2017)
Value function (off-policy) methods ~1,000,000 ~1,500,000 (Gu et al. 2018)
(model-based) ~30,000 ~400,000 (PE-TS, Kurtland Chua et al. 2018)

Table 1: Relative sample efficiency of various RL algorithm families.

Sample efficiency varies widely between implementations within the same class of algorithm, and I found that the estimates from the slide can be somewhat exaggerated with respect to specific examples in the literature. In particular, OpenAI’s evolutionary strategies paper actually reported a better sample efficiency than TRPO, a policy gradient method that they used as a comparison. Their reported solution for HalfCheetah took 3 million timesteps, a far cry from Levine’s estimate of 1 billion.

 

On the other hand, a related paper published by Uber AI labs that applied genetic algorithms to Atari games found sample efficiencies that were around the 1 billion time steps mark, about 5 times greater than the value-function algorithm they compared with and in line with Levine’s estimates from the course.

 

More is Less in Some Cases – Learning from Evolution

 

In the example discussed above, evolutionary strategies are among the most sample-inefficient methods available, typically requiring at least 10 times more steps to learn a given task than other approaches. On the other end of the spectrum, model-based and imitation methods require the least amount of time steps to learn the same task.

At first glance, it appears to be an open and shut case against the utility of evolution-based methods, but a funny thing happens when you optimize for compute instead of sample efficiency. Due to the decreased overhead of running evolutionary strategies, which don’t even require a backpropagation pass, they can actually require less compute. They are also inherently parallelizable. Because each episode or individual agent in a population does not depend on the results of other agents/episodes, the learning algorithm becomes embarrassingly parallel. With a fast simulator, it may take substantially less time (as measured by the clock on your wall) to solve a given problem.

The InvertedPendulumSwingup task start and goal state. The green capsule slides along the yellow rod, with the goal of bringing the unactuated red pole to balance upright.

To give a rough comparison of computational efficiency, I ran several open source implementations of various learning algorithms on a cart-pole swing-up task InvertedPendulumSwingupBulletEnv-v0 from PyBullet. Code for the representative evolutionary algorithm, covariance matrix adaptation, is available on Github, while the other algorithms are all part of OpenAI’s Spinning Up in Deep RL resource.

The policy architectures were all kept the same: a feed-forward dense neural network with two hidden layers of 16 neurons each. I ran all algorithms on a single core of a modest Intel i5 2.4 GHz CPU, so the results can only really be compared to each other, and the differences in training time are without any parallelization speedup. It’s worth noting that OpenAI managed to train the MujoCo humanoid in 10 minutes on 1,440 workers with evolution strategies, so parallelization speedups are real and lucrative if you have the CPU cores for it.

 

Method family Algorithm Time steps to solve Time to solve (seconds)
Evolution strategies Covariance Matrix Adaptation

[code]

~4,100,000 ~500 s
Policy gradients Proximal Policy Optimization

[code]

~1,800,000 ~2000 s
Fully online actor-critic methods Soft Actor-Critic

[code]

~1,500,000 ~17,000 s
Value function (off-policy) methods Twin-Delayed DDPG

[code]

~2,000,000 ~17,500 s

Table 2: Comparing different learning methods wall-clock time and sample efficiency. 

The table above gives a good idea of the relative relationship between the required resources for different methods. The most sample efficient algorithm (soft actor-critic) required about half as many steps but consumed 34 times more CPU time. Twin-delayed DDPG (aka TD3) and soft actor-critic were less stable than the other methods.

 

We didn’t look at model-based RL algorithms when running experiments for Table 2 due to a lack of open source tools. Research progress in model-based RL suffers from closed source development and a lack of standard environments, but Wang et al. made a heroic effort to provide benchmarks for many model-based algorithms. They found that most model-based methods were able to solve a task they called Pendulum, very similar to the task reported in the table above, in about 25,000 steps. Compared to policy gradient methods, training (wall-clock) time was about 100 to 200 times longer for most model-based methods they investigated.

Although deep learning still seems to favor “fancy” approaches to reinforcement learning, evolution-based methods have been making a comeback. OpenAI’s “Evolution Strategies as a Scalable Alternative to Reinforcement Learning” from 2016 was joined in 2017 by a large-scale demonstration of genetic algorithms learning to play Atari games. Without all the fancy mathematical trappings surrounding advanced RL algorithms, evolutionary algorithms are conceptually straightforward: generate a population and set the individual to some task, keep the best performers to seed the next generation, and repeat until a performance threshold is met. Due to the somewhat simple concepts behind them and their inherent parallelization potential, you may find that evolutionary algorithms will yield substantial savings in what is arguably your most scarce resource: developer time.

 

There Are Some Caveats to Know About Compute & Sample Efficiency

 

Direct comparisons of compute and sample efficiency between different RL algorithms on a single task isn’t entirely fair due to the many variables which can differ between implementations. One algorithm may converge earlier but never reach the same score as a different, slower algorithm, and in general, you can bet that in any published RL work, the authors spent a lot more effort optimizing and experimenting with their new method than any of the comparison algorithms.

However, the examples we discussed above give us a good idea of what to expect from reinforcement learning agents. Model-based methods, while promising, are not mature compared to other options and may not be worth the additional effort for most tasks. Perhaps surprisingly, evolutionary algorithms perform well on a variety of tasks and shouldn’t be ignored because of the perception they are “old-fashioned” or “too simple.” When considering the value of all available resources and their consumption by available methods, evolutionary algorithms may indeed offer the best return.

Original. Reposted with permission.

 

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