Projective simulation is a model for intelligent agents with a deliberation capacity that is based on episodic memory. The model has been shown to provide a flexible framework for constructing reinforcement-learning agents, and it allows for quantum mechanical generalization, which leads to a speedup in deliberation time. Projective simulation agents have been applied successfully in the context of complex skill learning in robotics and the design of the state-of-the-art quantum experiments. In this paper, we study the performance of projective simulation in two benchmarking problems in navigation, namely, the grid world and the mountain car problem. The performance of projective simulation is compared to standard tabular reinforcement learning approaches, Q-learning, and SARSA. Our comparison demonstrates that the performance of projective simulation and standard learning approaches are qualitatively and quantitatively similar, while it is much easier to choose optimal model parameters in the case of projective simulation with reduced computational effort of one to two orders of magnitude. Our results show that the projective simulation model stands out for its simplicity in terms of the number of model parameters, which makes it simple to set up the learning agent in unknown task environments.
Projective simulation is a model for intelligent agents with a deliberation capacity that is based on episodic memory. The model has been shown to provide a flexible framework for constructing reinforcement-learning agents, and it allows for quantum mechanical generalization, which leads to a speedup in deliberation time. Projective simulation agents have been applied successfully in the context of complex skill learning in robotics and the design of the state-of-the-art quantum experiments. In this paper, we study the performance of projective simulation in two benchmarking problems in navigation, namely, the grid world and the mountain car problem. The performance of projective simulation is compared to standard tabular reinforcement learning approaches, Q-learning, and SARSA. Our comparison demonstrates that the performance of projective simulation and standard learning approaches are qualitatively and quantitatively similar, while it is much easier to choose optimal model parameters in the case of projective simulation with reduced computational effort of one to two orders of magnitude. Our results show that the projective simulation model stands out for its simplicity in terms of the number of model parameters, which makes it simple to set up the learning agent in unknown task environments.
The ability to generalize is an important feature of any intelligent agent. Not only because it may allow the agent to cope with large amounts of data, but also because in some environments, an agent with no generalization capabilities cannot learn. In this work we outline several criteria for generalization, and present a dynamic and autonomous machinery that enables projective simulation agents to meaningfully generalize. Projective simulation, a novel, physical approach to artificial intelligence, was recently shown to perform well in standard reinforcement learning problems, with applications in advanced robotics as well as quantum experiments. Both the basic projective simulation model and the presented generalization machinery are based on very simple principles. This allows us to provide a full analytical analysis of the agent's performance and to illustrate the benefit the agent gains by generalizing. Specifically, we show that already in basic (but extreme) environments, learning without generalization may be impossible, and demonstrate how the presented generalization machinery enables the projective simulation agent to learn.
In recent years, the interest in leveraging quantum effects for enhancing machine learning tasks has significantly increased. Many algorithms speeding up supervised and unsupervised learning were established. The first framework in which ways to exploit quantum resources specifically for the broader context of reinforcement learning were found is projective simulation. Projective simulation presents an agent-based reinforcement learning approach designed in a manner which may support quantum walk-based speedups. Although classical variants of projective simulation have been benchmarked against common reinforcement learning algorithms, very few formal theoretical analyses have been provided for its performance in standard learning scenarios. In this paper, we provide a detailed formal discussion of the properties of this model. Specifically, we prove that one version of the projective simulation model, understood as a reinforcement learning approach, converges to optimal behavior in a large class of Markov decision processes. This proof shows that a physically inspired approach to reinforcement learning can guarantee to converge.
We utilize hybrid quantum deep reinforcement learning to learn navigation tasks for a simple, wheeled robot in simulated environments of increasing complexity. For this, we train parameterized quantum circuits (PQCs) with two different encoding strategies in a hybrid quantum-classical setup as well as a classical neural network baseline with the double deep Q network (DDQN) reinforcement learning algorithm. Quantum deep reinforcement learning (QDRL) has previously been studied in several relatively simple benchmark environments, mainly from the OpenAI gym suite. However, scaling behavior and applicability of QDRL to more demanding tasks closer to real-world problems e.g., from the robotics domain, have not been studied previously. Here, we show that quantum circuits in hybrid quantum-classic reinforcement learning setups are capable of learning optimal policies in multiple robotic navigation scenarios with notably fewer trainable parameters compared to a classical baseline. Across a large number of experimental configurations, we find that the employed quantum circuits outperform the classical neural network baselines when equating for the number of trainable parameters. Yet, the classical neural network consistently showed better results concerning training times and stability, with at least one order of magnitude of trainable parameters more than the best-performing quantum circuits. However, validating the robustness of the learning methods in a large and dynamic environment, we find that the classical baseline produces more stable and better performing policies overall. For the two encoding schemes, we observed better results for consecutively encoding the classical state vector on each qubit compared to encoding each component on a separate qubit. Our findings demonstrate that current hybrid quantum machine-learning approaches can be scaled to simple robotic problems while yielding sufficient results, at least in an idealized simulated setting, but there are yet open questions regarding the application to considerably more demanding tasks. We anticipate that our work will contribute to introducing quantum machine learning in general and quantum deep reinforcement learning in particular to more demanding problem domains and emphasize the importance of encoding techniques for classic data in hybrid quantum-classical settings.
Abstract Projective Simulation (PS) is a model for agency that incorporates aspects of reinforcement learning, an indeterministic basic dynamics inspired by physical hopping processes as studied in quantum optics, and an overall orientation towards agency as a continuous process of interaction with the environment as described by phenomenology. We explain the formal structure of PS in detail and compare it to the more standard paradigm of reinforcement learning. PS stands out mostly due to its specific memory structure (Episodic and Compositional Memory, ECM) and its openness, which makes it apt as an agency model rather than just a learning model: PS does not start from a fixed environment model to be “solved”. The focus is, rather, on the internal dynamics of deliberation, which is resolved as a stochastic process within the ECM, as well as on learning and adaptation over a long time, allowing for significant and even disruptive changes in the environment to be incorporated. After discussing the model, we showcase several applications of PS, prominently in basic research in quantum mechanics and especially in quantum information. This strengthens our claim about the intimate connection between agency and quantum physics that we already defended in Chaps. 3 and 4 . We also consider quantum versions of PS, which promise to show quantum advantages in machine learning while retaining a maximum of transparency. These applications motivate a separate discussion of transparency and traceability in the context of explainable (quantum) AI.
A scheme that successfully employs quantum mechanics in the design of autonomous learning agents has recently been reported in the context of the projective simulation (PS) model for artificial intelligence. In that approach, the key feature of a PS agent, a specific type of memory which is explored via random walks, was shown to be amenable to quantization, allowing for a speed-up. In this work we propose an implementation of such classical and quantum agents in systems of trapped ions. We employ a generic construction by which the classical agents are 'upgraded' to their quantum counterparts by a nested process of adding coherent control, and we outline how this construction can be realized in ion traps. Our results provide a flexible modular architecture for the design of PS agents. Furthermore, we present numerical simulations of simple PS agents which analyze the robustness of our proposal under certain noise models.
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.