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arXiv:2209.11044 · Quantum Science and Technology

Hybrid actor-critic algorithm for quantum reinforcement learning at CERN beam lines

Michael Schenk, Elías F. Combarro, Michele Grossi, Verena Kain, Kevin Shing Bruce Li, Mircea-Marian Popa, Sofia Vallecorsa

Published Feb 5, 2024• 19 citations
arXivHTMLPDF

Abstract

Abstract Free energy-based reinforcement learning (FERL) with clamped quantum Boltzmann machines (QBM) was shown to significantly improve the learning efficiency compared to classical Q-learning with the restriction, however, to discrete state-action space environments. In this paper, the FERL approach is extended to multi-dimensional continuous state-action space environments to open the doors for a broader range of real-world applications. First, free energy-based Q-learning is studied for discrete action spaces, but continuous state spaces and the impact of experience replay on sample efficiency is assessed. In a second step, a hybrid actor-critic (A-C) scheme for continuous state-action spaces is developed based on the deep deterministic policy gradient algorithm combining a classical actor network with a QBM-based critic. The results obtained with quantum annealing (QA), both simulated and with D-Wave QA hardware, are discussed, and the performance is compared to classical reinforcement learning methods. The environments used throughout represent existing particle accelerator beam lines at the European Organisation for Nuclear Research. Among others, the hybrid A-C agent is evaluated on the actual electron beam line of the Advanced Wakefield Experiment (AWAKE).

DOI
10.1088/2058-9565/ad261b

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Abstract Free energy-based reinforcement learning (FERL) with clamped quantum Boltzmann machines (QBM) was shown to significantly improve the learning efficiency compared to classical Q-learning with the restriction, however, to discrete state-action space environments. In this paper, the FERL approach is extended to multi-dimensional continuous state-action space environments to open the doors for a broader range of real-world applications. First, free energy-based Q-learning is studied for discrete action spaces, but continuous state spaces and the impact of experience replay on sample efficiency is assessed. In a second step, a hybrid actor-critic (A-C) scheme for continuous state-action spaces is developed based on the deep deterministic policy gradient algorithm combining a classical actor network with a QBM-based critic. The results obtained with quantum annealing (QA), both simulated and with D-Wave QA hardware, are discussed, and the performance is compared to classical reinforcement learning methods. The environments used throughout represent existing particle accelerator beam lines at the European Organisation for Nuclear Research. Among others, the hybrid A-C agent is evaluated on the actual electron beam line of the Advanced Wakefield Experiment (AWAKE).
Quantum reinforcement learning (QRL), a cutting-edge field at the intersection of quantum computing and artificial intelligence, has the potential to revolutionize domains like chemistry and autonomous systems with its computational advantages. The free energy-based reinforcement learning algorithm (FERL) is a QRL algorithm inspired by the classical deep Q-learning algorithm (DQN) which uses a quantum Boltzmann machine (QBM) as the Q-function with quantum annealing (QA) as the solver. It has demonstrated considerable advantage compared to its classical counterpart DQN. The aim of this project is exploring the replacement of QA with the quantum approximate optimization algorithm (QAOA) and its recursive variant (RQAOA). We focus on the one-dimensional beam target steering control task based on the beam optics of the TT24-T4 transfer line at CERN. We perform and compare simulations of QA and QAOA, obtaining successful results for both QAOA and RQAOA, noticing that the performance of FERL using RQAOA for p=1 as a solver is very similar to the obtained through simulated QA for this scenario. The success of this experiment might lead the application of the QAOA solver to the hybrid actor-critic algorithm in development at CERN which allows to tackle control tasks using a continuous action space.
Quantum computing has a superior advantage in tackling specific problems, such as integer factorization and Simon's problem. For more general tasks in machine learning, by applying variational quantum circuits, more and more quantum algorithms have been proposed recently, especially in supervised learning and unsupervised learning. However, little work has been done in reinforcement learning, arguably more important and challenging. Previous work in quantum reinforcement learning mainly focuses on discrete control tasks where the action space is discrete. In this work, we develop a quantum reinforcement learning algorithm based on soft actor-critic -- one of the state-of-the-art methods for continuous control. Specifically, we use a hybrid quantum-classical policy network consisting of a variational quantum circuit and a classical artificial neural network. Tested in a standard reinforcement learning benchmark, we show that this quantum version of soft actor-critic is comparable with the original soft actor-critic, using much less adjustable parameters. Furthermore, we analyze the effect of different hyper-parameters and policy network architectures, pointing out the importance of architecture design for quantum reinforcement learning.
We introduce theoretically grounded Continuous Semi-Quantum Boltzmann Machines (CSQBMs) that supports continuous-action reinforcement learning. By combining exponential-family priors over visible units with quantum Boltzmann distributions over hidden units, CSQBMs yield a hybrid quantum-classical model that reduces qubit requirements while retaining strong expressiveness. Crucially, gradients with respect to continuous variables can be computed analytically, enabling direct integration into Actor-Critic algorithms. Building on this, we propose a continuous Q-learning framework that replaces global maximization by efficient sampling from the CSQBM distribution, thereby overcoming instability issues in continuous control.
Quantum computing offers efficient encapsulation of high-dimensional states. In this work, we propose a novel quantum reinforcement learning approach that combines the Advantage Actor-Critic algorithm with variational quantum circuits by substituting parts of the classical components. This approach addresses reinforcement learning's scalability concerns while maintaining high performance. We empirically test multiple quantum Advantage Actor-Critic configurations with the well known Cart Pole environment to evaluate our approach in control tasks with continuous state spaces. Our results indicate that the hybrid strategy of using either a quantum actor or quantum critic with classical post-processing yields a substantial performance increase compared to pure classical and pure quantum variants with similar parameter counts. They further reveal the limits of current quantum approaches due to the hardware constraints of noisy intermediate-scale quantum computers, suggesting further research to scale hybrid approaches for larger and more complex control tasks.
Reinforcement learning has driven impressive advances in machine learning. Simultaneously, quantum-enhanced machine learning algorithms using quantum annealing underlie heavy developments. Recently, a multi-agent reinforcement learning (MARL) architecture combining both paradigms has been proposed. This novel algorithm, which utilizes Quantum Boltzmann Machines (QBMs) for Q-value approximation has outperformed regular deep reinforcement learning in terms of time-steps needed to converge. However, this algorithm was restricted to single-agent and small 2x2 multi-agent grid domains. In this work, we propose an extension to the original concept in order to solve more challenging problems. Similar to classic DQNs, we add an experience replay buffer and use different networks for approximating the target and policy values. The experimental results show that learning becomes more stable and enables agents to find optimal policies in grid-domains with higher complexity. Additionally, we assess how parameter sharing influences the agents behavior in multi-agent domains. Quantum sampling proves to be a promising method for reinforcement learning tasks, but is currently limited by the QPU size and therefore by the size of the input and Boltzmann machine.
Classical reinforcement learning (RL) methods often struggle in complex, high-dimensional environments because of their extensive parameter requirements and challenges posed by stochastic, non-deterministic settings. This study introduces quantum deep reinforcement learning (QDRL) to train humanoid agents efficiently. While previous quantum RL models focused on smaller environments, such as wheeled robots and robotic arms, our work pioneers the application of QDRL to humanoid robotics, specifically in environments with substantial observation and action spaces, such as MuJoCo's Humanoid-v4 and Walker2d-v4. Using parameterized quantum circuits, we explored a hybrid quantum-classical setup to directly navigate high-dimensional state spaces, bypassing traditional mapping and planning. By integrating quantum computing with deep RL, we aim to develop models that can efficiently learn complex navigation tasks in humanoid robots. We evaluated the performance of the Soft Actor-Critic (SAC) in classical RL against its quantum implementation. The results show that the quantum SAC achieves an 8% higher average return (246.40) than the classical SAC (228.36) after 92% fewer steps, highlighting the accelerated learning potential of quantum computing in RL tasks.