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.
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.
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.
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.
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.
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.
Reward shaping is a critical component in reinforcement learning (RL), aiming to guide agents towards desired behaviors by modifying the reward function. However, designing effective reward shaping functions can be a challenging and time-consuming process, often requiring significant domain expertise. This paper proposes a novel approach leveraging quantum-inspired optimization techniques to automate and improve the reward shaping process for RL agents. Specifically, we utilize amplitude estimation, a technique inspired by quantum computing, to iteratively refine reward functions based on agent interactions. The core idea is to treat the reward function as a parameter to be optimized using a quantum-inspired algorithm, effectively learning a reward function that best aligns with the agent's learning objective. We demonstrate, through theoretical analysis and a conceptual framework, the potential benefits of this approach in accelerating learning and improving the efficiency of RL algorithms. The proposed method offers a promising alternative to traditional reward shaping techniques, particularly in complex environments where designing hand-crafted reward functions is difficult. The evaluation of this approach is left for future work, focusing on practical implementation and comparative analysis with existing reward shaping strategies.
This paper investigates the application of reinforcement learning (RL) for adaptive quantum control. Traditional quantum control methods often rely on pre-designed pulse shapes optimized for specific scenarios, lacking adaptability to variations in system parameters or environmental noise. This work proposes a novel framework where an RL agent learns to dynamically adjust quantum control pulses in real-time, maximizing the fidelity of quantum operations. The agent receives feedback from the quantum system, typically measured through state variables, and utilizes this information to optimize the control pulse sequence. This adaptive approach addresses the limitations of static control schemes and promises enhanced robustness and performance in complex quantum systems. The core claim centers on utilizing reinforcement learning to design optimal quantum control pulses. The central mechanism involves a trained controller dynamically adjusting pulses based on system feedback. The presented methodology offers a new approach to quantum control, particularly relevant in noisy environments and systems with parameter variations. The research demonstrates the potential of RL for achieving superior quantum control outcomes compared to conventional techniques. ---