In Quantum Reinforcement Learning, the "hybrid agent for quantum-accessible reinforcement learning" (Hamann and Wölk, 2022) provides a quadratic speed-up in terms of sample complexity over classical algorithms. This hybrid agent may be used in deterministic and strictly episodic environments, for which the maze problem is a standard example. With the current algorithm, however, the episode length (i.e., the number of actions to be played in an episode) is a hyperparameter which needs to be set. For scenarios such as mazes with an unknown distance towards the goal, this poses a problem, since a feasible episode length value is not known initially. In this work, we propose an adaption to the hybrid algorithm that uses a variable episode length selection strategy, allowing its usage in a wider range of maze problem scenarios. We test our novel approach against classical agents in various maze scenarios. Finally, we reason about conditions for which a quantum advantage persists.
In Quantum Reinforcement Learning, the "hybrid agent for quantum-accessible reinforcement learning" (Hamann and Wölk, 2022) provides a quadratic speed-up in terms of sample complexity over classical algorithms. This hybrid agent may be used in deterministic and strictly episodic environments, for which the maze problem is a standard example. With the current algorithm, however, the episode length (i.e., the number of actions to be played in an episode) is a hyperparameter which needs to be set. For scenarios such as mazes with an unknown distance towards the goal, this poses a problem, since a feasible episode length value is not known initially. In this work, we propose an adaption to the hybrid algorithm that uses a variable episode length selection strategy, allowing its usage in a wider range of maze problem scenarios. We test our novel approach against classical agents in various maze scenarios. Finally, we reason about conditions for which a quantum advantage persists.
Abstract The “hybrid agent for quantum-accessible reinforcement learning,” as defined in (Hamann and Wölk New J Phys 24:033044 2022), provides a proven quasi-quadratic speedup and is experimentally tested. However, the standard version can only be applied to episodic learning tasks with fixed episode length. In many real-world applications, the information about the necessary number of steps within an episode to reach a defined target is not available in advance and especially before reaching the target for the first time. Furthermore, in such scenarios, classical agents have the advantage of observing at which step they reach the target. How to best deal with an unknown target distance in classical and quantum reinforcement learning and whether the hybrid agent can provide an advantage in such learning scenarios is unknown so far. In this work, we introduce a hybrid agent with a stochastic episode length selection strategy to alleviate the need for knowledge about the necessary episode length. Through simulations, we test the adapted hybrid agent’s performance versus classical counterparts with and without similar episode selection strategies. Our simulations demonstrate a speedup in certain scenarios due to our developed episode length selection strategy for classical learning agents as well as an additional speedup for our resulting hybrid learning agent.
Combining quantum computing techniques in the form of amplitude amplification with classical reinforcement learning has led to the so-called “hybrid agent for quantum-accessible reinforcement learning”, which achieves a quadratic speedup in sample complexity for certain learning problems. So far, this hybrid agent has only been applied to stationary learning problems, that is, learning problems without any time dependency within components of the Markov decision process. In this work, we investigate the applicability of the hybrid agent to dynamic RL environments and thus to more realistic scenarios. To this end, we enhance the hybrid agent by introducing a dissipation mechanism and, with the resulting learning agent, perform an empirical comparison with a classical RL agent in an RL environment with a time-dependent reward function. Our findings suggest that the modified hybrid agent can adapt its behavior to changes in the environment quickly, leading to a higher average success probability compared to its classical counterpart.
In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects of supervised, unsupervised and reinforcement learning. Reinforcement learning offers numerous options of how quantum theory can be applied, and is arguably the least explored, from a quantum perspective. Here, an agent explores an environment and tries to find a behavior optimizing some figure of merit. Some of the first approaches investigated settings where this exploration can be sped-up, by considering quantum analogs of classical environments, which can then be queried in superposition. If the environments have a strict periodic structure in time (i.e. are strictly episodic), such environments can be effectively converted to conventional oracles encountered in quantum information. However, in general environments, we obtain scenarios that generalize standard oracle tasks. In this work, we consider one such generalization, where the environment is not strictly episodic, which is mapped to an oracle identification setting with a changing oracle. We analyze this case and show that standard amplitude-amplification techniques can, with minor modifications, still be applied to achieve quadratic speed-ups. In addition, we prove that an algorithm based on Grover iterations is optimal for oracle identification even if the oracle changes over time in a way that the "rewarded space" is monotonically increasing. This result constitutes one of the first generalizations of quantum-accessible reinforcement learning.
Abstract Quantum machine learning (QML) is a young but rapidly growing field where quantum information meets machine learning. Here, we will introduce a new QML model generalising the classical concept of reinforcement learning to the quantum domain, i.e. quantum reinforcement learning (QRL). In particular, we apply this idea to the maze problem, where an agent has to learn the optimal set of actions in order to escape from a maze with the highest success probability. To perform the strategy optimisation, we consider a hybrid protocol where QRL is combined with classical deep neural networks. In particular, we find that the agent learns the optimal strategy in both the classical and quantum regimes, and we also investigate its behaviour in a noisy environment. It turns out that the quantum speedup does robustly allow the agent to exploit useful actions also at very short time scales, with key roles played by the quantum coherence and the external noise. This new framework has the high potential to be applied to perform different tasks (e.g. high transmission/processing rates and quantum error correction) in the new-generation noisy intermediate-scale quantum (NISQ) devices whose topology engineering is starting to become a new and crucial control knob for practical applications in real-world problems. This work is dedicated to the memory of Peter Wittek.
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. Using the paradigm of quantum accelerators, we introduce a routine that runs on a quantum computer, which allows for the encoding of probability distributions. This quantum routine is then employed, in a reinforcement learning set-up, to encode the distributions that drive action choices. Our routine is well-suited in the case of a large, although finite, number of actions and can be employed in any scenario where a probability distribution with a large support is needed. We describe the routine and assess its performance in terms of computational complexity, needed quantum resource, and accuracy. Finally, we design an algorithm showing how to exploit it in the context of Q-learning.
Abstract In the last decade quantum machine learning has provided fascinating and fundamental improvements to supervised, unsupervised and reinforcement learning (RL). In RL, a so-called agent is challenged to solve a task given by some environment. The agent learns to solve the task by exploring the environment and exploiting the rewards it gets from the environment. For some classical task environments, an analogue quantum environment can be constructed which allows to find rewards quadratically faster by applying quantum algorithms. In this paper, we analytically analyze the behavior of a hybrid agent which combines this quadratic speedup in exploration with the policy update of a classical agent. This leads to a faster learning of the hybrid agent compared to the classical agent. We demonstrate that if the classical agent needs on average ⟨J⟩ rewards and ⟨T⟩cl epochs to learn how to solve the task, the hybrid agent will take ⟨ T ⟩ q ⩽ α s α o ⟨ T ⟩ c l ⟨ J ⟩ epochs on average. Here, α s and α o denote constants depending on details of the quantum search and are independent of the problem size. Additionally, we prove that if the environment allows for maximally α o k max sequential coherent interactions, e.g. due to noise effects, an improvement given by ⟨T⟩q ≈ α o ⟨T⟩cl/(4k max) is still possible.