Monthly Archives: November 2021

Posted by Ted Baltz, Senior Staff Software Engineer, Google Research

For more than 70 years, plasma physicists have dreamed of controlled “breakeven” fusion, where a system is capable of releasing more energy in a fusion reaction than it takes to initiate and sustain those reactions. The challenge is that the reactor must create a plasma at a temperature of tens of millions of degrees, which requires a highly complex, finely tuned system to confine and sustain. Further, creating the plasma and maintaining it, requires substantial amounts of energy, which, to date, have exceeded that released in the fusion reaction itself. Nevertheless, if a “breakeven” system could be achieved, it could provide ample zero-carbon electricity, the potential impact of which has driven interest by government laboratories, such as ITER and the National Ignition Facility, as well as several privately funded efforts.

Today we highlight two recently published papers arising from our collaboration with TAE Technologies¹, which demonstrate exciting advancements in the field. In “Overview of C-2W: High-temperature, steady-state beam-driven field-reversed configuration plasmas,” published in Nuclear Fusion, we describe the experimental program implemented by TAE, which leverages our improved version of the Optometrist Algorithm for machine optimization. Due in part to this contribution, the current state-of-the-art reactor is able to achieve plasma lifetimes up to three times longer than its predecessor. In “Multi-instrument Bayesian reconstruction of plasma shape evolution in the C-2W experiment,” published in Physics of Plasmas, we detail new methods developed for analyzing indirect measurements of plasma to reconstruct its properties in detail. This work enabled us to better understand how instabilities in the plasma arise and to understand how to mitigate these perturbations in practice.

Optimizing the Next Generation Fusion Device
The C-2W “Norman” machine (named for TAE’s late co-founder Prof. Norman Rostoker) is a nearly complete rebuild of the C-2U machine that we described in 2017. For this updated version, the TAE team integrated new pressure vessels, new power supplies, a new vacuum system, along with other substantial upgrades.

Norman is incredibly complex, with over 1000 machine control parameters, and likewise, it captures extensive amounts of data for each run, including over 1000 measurements of conditions in the plasma alone. And while the measurements of each plasma experiment are extremely rich, there is no simple metric for “goodness”. Further complicating matters, it is not possible to rapidly iterate to improve performance, because only one experiment can be executed every eight minutes. For these reasons, tuning the system is quite difficult and relies on the expert intuition developed by the plasma physicists operating the system. To optimize the new reactor’s performance, we needed a control system capable of handling the tremendous complexity of the system while being able to quickly tune the control parameters in response to the extensive data generated in experiments.

To accomplish this, we further adapted the Optometrist Algorithm that we had developed for the C-2U system to leverage the expertise of the operators. In this algorithm, the physicists compare experiment pairs, and determine whether the trial better achieves the current goals of the experiment, according to their judgment, than the current reference experiment — e.g., achieving increased plasma size at a fixed temperature, increased temperature, etc. By updating the reference accordingly, machine performance improves over time. However, accounting for operator intuition during this process is critical, because the measure of improvement may not be immediately obvious. For example, under some situations, an experiment with much denser plasma that is a little bit colder may, in fact, be “better”, because it may lead to other improvements in subsequent experiments. We further modified the algorithm by fitting a logistic regression to the binary decisions of the expert to guide the trial experiments, making a classic exploration-exploitation tradeoff.

Applying the Optometrist Algorithm to the magnetic field coils that form the plasma, we found a novel timing sequence that provides consistent starting conditions for long-lived plasmas, almost tripling the plasma lifetime when first applied. This was a marked improvement over the regime of net plasma heating first seen on the C-2U machine in 2015.

Plasma formation section of the Norman reactor. The outer coils operate for the duration of the experiments while the inner coils accelerate the plasma in less than 10 microseconds. (Photograph by Erik Lucero)

Bayesian Reconstruction of Plasma Conditions
In addition to optimizing the performance of the machine, we also sought to more thoroughly understand the behavior of the plasmas it is generating. This includes understanding the density profiles, separate electron and ion temperatures, and magnetic fields generated by the plasma. Because the plasma in a fusion generator reaches 30 million Kelvin, which would destroy most solid materials in moments, precise measurements of the plasma conditions are very difficult.

To address this, Norman has a set of indirect diagnostics, generating 5 GB of data per shot, that peer into the plasma without touching it. One of these is a two-story laser interferometer that measures the line-integrated electron density along 14 lines of sight through the plasma, with a sample rate of more than a megahertz. The resulting dataset of line-integrated densities can be used to extract the spatial density profile of the plasma, which is crucial to understanding the plasma behavior. In this case, the Norman reactor generates field-reversed configuration (FRC) plasmas that tend to be best confined when they are hollow (imagine a smoke ring elongated into a barrel shape). The challenge in this situation is that generating the spatial density profiles for such a plasma configuration is an inverse problem, i.e., it is more difficult to infer the shape of the plasma from the measurements (the “inverse” direction) than to predict the measurements from a known shape (the “forward” direction).

Schematic of C-2W confinement vessel showing measurement systems: interferometer lines of sight measuring electron density (magenta), neutral particle beam lines of sight measuring ion density (purple) and magnetic sensors (blue). These disparate measurements are combined in the Bayesian framework.

We developed a TensorFlow implementation of the Hamiltonian Monte Carlo (HMC) algorithm to address the problem of inferring the density profile of the plasma from multiple indirect measurements. Because the plasma is described by hundreds to thousands of variables and we want to reconstruct the state for thousands of frames, linked into “bursts” or short movies, for each plasma experiment, processing on CPUs is insufficient. For this reason, we optimized the HMC algorithm to be executed on GPUs. The Bayesian framework for this involves building “forward” models (i.e., predicting effects from causes) for several instruments, which can predict what the instrument would record, given some specified plasma conditions. We can then use HMC to calculate the probabilities of various possible plasma conditions. Understanding both density and temperature are crucial to the problem of breakeven fusion.

High Frequency Plasma Perturbations
Reconstruction of the plasma conditions does more than just recover the plasma density profile, it also recovers the behavior of high frequency density perturbations in the plasma. TAE has done a large number of experiments to determine if Norman’s neutral particle beams and electrode currents can control these oscillations. In the second paper, we demonstrate the strong mitigating effects of the neutral beams, showing that when the neutral beams are turned off, fluctuations immediately begin growing. The reconstruction allows us to see how the radial density profile of the plasma evolves as the perturbations grow, an understanding of which is key to mitigating such perturbations, allowing long-lived stable plasmas. Following a long tradition of listening to plasma perturbations to better intuit their behavior (e.g., ionospheric “whistlers” have been captured by radio operators for over a century), we translate the perturbations to audio (slowed down 500x) in order to listen to them.

The Future Looks Hot and Stable
With our assistance using machine optimization and data science, TAE achieved their major goals for Norman, which brings us a step closer to the goal of breakeven fusion. The machine maintains a stable plasma at 30 million Kelvin for 30 milliseconds, which is the extent of available power to its systems. They have completed a design for an even more powerful machine, which they hope will demonstrate the conditions necessary for breakeven fusion before the end of the decade. TAE has succeeded with two complete machine builds during our collaboration, and we are really excited to see the third.

Acknowledgments
We wish to thank Michael Dikovsky, Ian Langmore, Peter Norgaard, Scott Geraedts, Rob von Behren, Bill Heavlin, Anton Kast, Tom Madams, John Platt, Ross Koningstein, and Matt Trevithick for their contributions to this work. We thank the TensorFlow Probability team for considerable implementation assistance. Furthermore, we thank Jeff Dean for visiting TAE’s facility in Southern California and providing thoughtful suggestions. As always we are grateful to our colleagues at TAE Technologies for the opportunity to work on such a fascinating and important problem.

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Posted by Johan Ferret, Student Researcher, Google Research, Brain Team

An approach commonly used to train agents for a range of applications from robotics to chip design is reinforcement learning (RL). While RL excels at discovering how to solve tasks from scratch, it can struggle in training an agent to understand the reversibility of its actions, which can be crucial to ensure that agents behave in a safe manner within their environment. For instance, robots are generally costly and require maintenance, so one wants to avoid taking actions that might lead to broken components. Estimating if an action is reversible or not (or better, how easily it can be reversed) requires a working knowledge of the physics of the environment in which the agent is operating. However, in the standard RL setting, agents do not possess a model of the environment sufficient to do this.

In “There Is No Turning Back: A Self-Supervised Approach to Reversibility-Aware Reinforcement Learning”, accepted at NeurIPS 2021, we present a novel and practical way of approximating the reversibility of agent actions in the context of RL. This approach, which we call Reversibility-Aware RL, adds a separate reversibility estimation component to the RL procedure that is self-supervised (i.e., it learns from unlabeled data collected by the agents). It can be trained either online (jointly with the RL agent) or offline (from a dataset of interactions). Its role is to guide the RL policy towards reversible behavior. This approach increases the performance of RL agents on several tasks, including the challenging Sokoban puzzle game.

Reversibility-Aware RL
The reversibility component added to the RL procedure is learned from interactions, and crucially, is a model that can be trained separate from the agent itself. The model training is self-supervised and does not require that the data be labeled with the reversibility of the actions. Instead, the model learns about which types of actions tend to be reversible from the context provided by the training data alone.We call the theoretical explanation for this empirical reversibility, a measure of the probability that an event A precedes another event B, knowing that A and B both happen. Precedence is a useful proxy for true reversibility because it can be learned from a dataset of interactions, even without rewards.

Imagine, for example, an experiment where a glass is dropped from table height and when it hits the floor it shatters. In this case, the glass goes from position A (table height) to position B (floor) and regardless of the number of trials, A always precedes B, so when randomly sampling pairs of events, the probability of finding a pair in which A precedes B is 1. This would indicate an irreversible sequence. Assume, instead, a rubber ball was dropped instead of the glass. In this case, the ball would start at A, drop to B, and then (approximately) return to A. So, when sampling pairs of events, the probability of finding a pair in which A precedes B would only be 0.5 (the same as the probability that a random pair showed B preceding A), and would indicate a reversible sequence.

Reversibility estimation relies on the knowledge of the dynamics of the world. A proxy to reversibility is precedence, which establishes which of two events comes first on average,given that both are observed.

In practice, we sample pairs of events from a collection of interactions, shuffle them, and train the neural network to reconstruct the actual chronological order of the events. The network’s performance is measured and refined by comparing its predictions against the ground truth derived from the timestamps of the actual data. Since events that are temporally distant tend to be either trivial or impossible to order, we sample events in a temporal window of fixed size. We then use the prediction probabilities of this estimator as a proxy for reversibility: if the neural network’s confidence that event A happens before event B is higher than a chosen threshold, then we deem that the transition from event A to B is irreversible.

Precedence estimation consists of predicting the temporal order of randomly shuffled events.

Integrating Reversibility into RL
We propose two concurrent ways of integrating reversibility in RL:

1. Reversibility-Aware Exploration (RAE): This approach penalizes irreversible transitions, via a modified reward function. When the agent picks an action that is considered irreversible, it receives a reward corresponding to the environment’s reward minus a positive, fixed penalty, which makes such actions less likely, but does not exclude them.
2. Reversibility-Aware Control (RAC): Here, all irreversible actions are filtered out, a process that serves as an intermediate layer between the policy and the environment. When the agent picks an action that is considered irreversible, the action selection process is repeated, until a reversible action is chosen.

The proposed RAE (left) and RAC (right) methods for reversibility-aware RL.

An important distinction between RAE and RAC is that RAE only encourages reversible actions, it does not prohibit them, which means that irreversible actions can still be performed when the benefits outweigh costs (as in the Sokoban example below). As a result, RAC is better suited for safe RL where irreversible side-effects induce risks that should be avoided entirely, and RAE is better suited for tasks where it is suspected that irreversible actions are to be avoided most of the time.

To illustrate the distinction between RAE and RAC, we evaluate the capabilities of both proposed methods. A few example scenarios follow:

• Avoiding (but not prohibiting) irreversible side-effects

  A general rule for safe RL is to minimize irreversible interactions when possible, as a principle of caution. To test such capabilities, we introduce a synthetic environment where an agent in an open field is tasked with reaching a goal. If the agent follows the established pathway, the environment remains unchanged, but if it departs from the pathway and onto the grass, the path it takes turns to brown. While this changes the environment, no penalty is issued for such behavior.

  In this scenario, a typical model-free agent, such as a Proximal Policy Optimization (PPO) agent, tends to follow the shortest path on average and spoils some of the grass, whereas a PPO+RAE agent avoids all irreversible side-effects.

  Top-left: The synthetic environment in which the agent (blue) is tasked with reaching a goal (pink). A pathway is shown in grey leading from the agent to the goal, but it does not follow the most direct route between the two. Top-right: An action sequence with irreversible side-effects of an agent’s actions. When the agent departs from the path, it leaves a brown path through the field. Bottom-left: The visitation heatmap for a PPO agent. Agents tend to follow a more direct path than that shown in grey. Bottom-right: The visitation heatmap for a PPO+RAE agent. The irreversibility of going off-path encourages the agent to stay on the established grey path.

• Safe interactions by prohibiting irreversibility

  We also tested against the classic Cartpole task, in which the agent controls a cart in order to balance a pole standing precariously upright on top of it. We set the maximum number of interactions to 50k steps, instead of the usual 200. On this task, irreversible actions tend to cause the pole to fall, so it is better to avoid such actions at all.

  We show that combining RAC with any RL agent (even a random agent) never fails, given that we select an appropriate threshold for the probability that an action is irreversible. Thus, RAC can guarantee safe, reversible interactions from the very first step in the environment.

  We show how the Cartpole performance of a random policy equipped with RAC evolves with different threshold values (ꞵ). Standard model-free agents (DQN, M-DQN) typically score less than 3000, compared to 50000 (the maximum score) for an agent governed by a random+RAC policy at a threshold value of β=0.4.

• Avoiding deadlocks in Sokoban

  Sokoban is a puzzle game in which the player controls a warehouse keeper and has to push boxes onto target spaces, while avoiding unrecoverable situations (e.g., when a box is in a corner or, in some cases, along a wall).

  An action sequence that completes a Sokoban level. Boxes (yellow squares with a red “x”) must be pushed by an agent onto targets (red outlines with a dot in the middle). Because the agent cannot pull the boxes, any box pushed against a wall can be difficult, if not impossible to get away from the wall, i.e., it becomes “deadlocked”.

  For a standard RL model, early iterations of the agent typically act in a near-random fashion to explore the environment, and consequently, get stuck very often. Such RL agents either fail to solve Sokoban puzzles, or are quite inefficient at it.

  Agents that explore randomly quickly engage themselves in deadlocks that prevent them from completing levels (as an example here, pushing the rightmost box on the wall cannot be reversed).

  We compared the performance in the Sokoban environment of IMPALA, a state-of-the-art model-free RL agent, to that of an IMPALA+RAE agent. We find that the agent with the combined IMPALA+RAE policy is deadlocked less frequently, resulting in superior scores.

  The scores of IMPALA and IMPALA+RAE on a set of 1000 Sokoban levels. A new level is sampled at the beginning of each episode.The best score is level dependent and close to 10.

  In this task, detecting irreversible actions is difficult because it is a highly imbalanced learning problem — only ~1% of actions are indeed irreversible, and many other actions are difficult to flag as reversible, because they can only be reversed through a number of additional steps by the agent.

  Reversing an action is sometimes non-trivial. In the example shown here, a box has been pushed against the wall, but is still reversible. However, reversing the situation takes at least five separate movements comprising 17 distinct actions by the agent (each numbered move being the result of several actions from the agent).

  We estimate that approximately half of all Sokoban levels require at least one irreversible action to be completed (e.g., because at least one target destination is adjacent to a wall). Since IMPALA+RAE solves virtually all levels, it implies that RAE does not prevent the agent from taking irreversible actions when it is crucial to do so.

Conclusion
We present a method that enables RL agents to predict the reversibility of an action by learning to model the temporal order of randomly sampled trajectory events, which results in better exploration and control. Our proposed method is self-supervised, meaning that it does not necessitate any prior knowledge about the reversibility of actions, making it well suited to a variety of environments. In the future, we are interested in studying further how these ideas could be applied in larger scale and safety-critical applications.

Acknowledgements
We would like to thank our paper co-authors Nathan Grinsztajn, Philippe Preux, Olivier Pietquin and Matthieu Geist. We would also like to thank Bobak Shahriari, Théophane Weber, Damien Vincent, Alexis Jacq, Robert Dadashi, Léonard Hussenot, Nino Vieillard, Lukasz Stafiniak, Nikola Momchev, Sabela Ramos and all those who provided helpful discussion and feedback on this work.

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