Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning are possible when given quantum access to reinforcement learning environments. Yet, the applicability of quantum algorithms in this setting remains very limited, notably in environments with large state and action spaces. In this work, we design quantum algorithms to train state-of-the-art reinforcement learning policies by exploiting quantum interactions with an environment. However, these algorithms only offer full quadratic speed-ups in sample complexity over their classical analogs when the trained policies satisfy some regularity conditions. Interestingly, we find that reinforcement learning policies derived from parametrized quantum circuits are well-behaved with respect to these conditions, which showcases the benefit of a fully-quantum reinforcement learning framework.
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning are possible when given quantum access to reinforcement learning environments. Yet, the applicability of quantum algorithms in this setting remains very limited, notably in environments with large state and action spaces. In this work, we design quantum algorithms to train state-of-the-art reinforcement learning policies by exploiting quantum interactions with an environment. However, these algorithms only offer full quadratic speed-ups in sample complexity over their classical analogs when the trained policies satisfy some regularity conditions. Interestingly, we find that reinforcement learning policies derived from parametrized quantum circuits are well-behaved with respect to these conditions, which showcases the benefit of a fully-quantum reinforcement learning framework.
Variational quantum circuits have recently gained popularity as quantum machine learning models. While considerable effort has been invested to train them in supervised and unsupervised learning settings, relatively little attention has been given to their potential use in reinforcement learning. In this work, we leverage the understanding of quantum policy gradient algorithms in a number of ways. First, we investigate how to construct and train reinforcement learning policies based on variational quantum circuits. We propose several designs for quantum policies, provide their learning algorithms, and test their performance on classical benchmarking environments. Second, we show the existence of task environments with a provable separation in performance between quantum learning agents and any polynomial-time classical learner, conditioned on the widely-believed classical hardness of the discrete logarithm problem. We also consider more natural settings, in which we show an empirical quantum advantage of our quantum policies over standard neural-network policies. Our results constitute a first step towards establishing a practical near-term quantum advantage in a reinforcement learning setting. Additionally, we believe that some of our design choices for variational quantum policies may also be beneficial to other models based on variational quantum circuits, such as quantum classifiers and quantum regression models.
With the advent of real-world quantum computing, the idea that parametrized quantum computations can be used as hypothesis families in a quantum-classical machine learning system is gaining increasing traction. Such hybrid systems have already shown the potential to tackle real-world tasks in supervised and generative learning, and recent works have established their provable advantages in special artificial tasks. Yet, in the case of reinforcement learning, which is arguably most challenging and where learning boosts would be extremely valuable, no proposal has been successful in solving even standard benchmarking tasks, nor in showing a theoretical learning advantage over classical algorithms. In this work, we achieve both. We propose a hybrid quantum-classical reinforcement learning model using very few qubits, which we show can be effectively trained to solve several standard benchmarking environments. Moreover, we demonstrate, and formally prove, the ability of parametrized quantum circuits to solve certain learning tasks that are intractable to classical models, including current state-of-art deep neural networks, under the widely-believed classical hardness of the discrete logarithm problem.
Reinforcement learning is a growing field in AI with a lot of potential. Intelligent behavior is learned automatically through trial and error in interaction with the environment. However, this learning process is often costly. Using variational quantum circuits as function approximators potentially can reduce this cost. In order to implement this, we propose the quantum natural policy gradient (QNPG) algorithm - a second-order gradient-based routine that takes advantage of an efficient approximation of the quantum Fisher information matrix. We experimentally demonstrate that QNPG outperforms first-order based training on different Contextual Bandits environments regarding convergence speed and stability and moreover reduces the sample complexity. Furthermore, we provide evidence for the practical feasibility of our approach by training on a 12-qubit hardware device.
Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a γ-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy (π∗), the optimal value function (v∗), and the optimal Q-function (q∗), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy (ε) and two main parameters of the MDP: the effective time horizon (1−γ1) and the size of the action space (A). Moreover, we show that our quantum algorithm for computing q∗ is optimal by proving a matching quantum lower bound.
Parametrised quantum circuits offer expressive and data-efficient representations for machine learning. Due to quantum states residing in a high-dimensional Hilbert space, parametrised quantum circuits have a natural interpretation in terms of kernel methods. The representation of quantum circuits in terms of quantum kernels has been studied widely in quantum supervised learning, but has been overlooked in the context of quantum RL. This paper proposes the use of kernel policies and quantum policy gradient algorithms for quantum-accessible environments. After discussing the properties of such policies and a demonstration of classical policy gradient on a coherent policy in a quantum environment, we propose parametric and non-parametric policy gradient and actor-critic algorithms with quantum kernel policies in quantum environments. This approach, implemented with both numerical and analytical quantum policy gradient techniques, allows exploiting the many advantages of kernel methods, including data-driven forms for functions (and their gradients) as well as tunable expressiveness. The proposed approach is suitable for vector-valued action spaces and each of the formulations demonstrates a quadratic reduction in query complexity compared to their classical counterparts. We propose actor-critic algorithms based on stochastic policy gradient, deterministic policy gradient, and natural policy gradient, and demonstrate additional query complexity reductions compared to quantum policy gradient algorithms under favourable conditions.
Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the task of choosing an optimal policy --- a function that tells the agent which action to take. In this work, we study two types of MDPs --- finite-horizon and infinite-horizon discounted --- and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum maximum finding, overall enhanced with techniques from sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.