Daniel Hein

Simon Wiedemann, Daniel Hein, Steffen Udluft et al.

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows that, given access to error-free, efficient quantum realizations of the agent and environment, quantum methods can yield provable improvements over classical Monte-Carlo based methods in terms of sample complexity. Our approach shows in detail how to combine amplitude estimation and Grover search into a policy evaluation and improvement scheme. We first develop quantum policy evaluation (QPE) which is quadratically more efficient compared to an analogous classical Monte Carlo estimation and is based on a quantum mechanical realization of a finite Markov decision process (MDP). Building on QPE, we derive a quantum policy iteration that repeatedly improves an initial policy using Grover search until the optimum is reached. Finally, we present an implementation of our algorithm for a two-armed bandit MDP which we then simulate.

Marc Weber, Phillip Swazinna, Daniel Hein et al.

Offline reinforcement learning provides a viable approach to obtain advanced control strategies for dynamical systems, in particular when direct interaction with the environment is not available. In this paper, we introduce a conceptual extension for model-based policy search methods, called variable objective policy (VOP). With this approach, policies are trained to generalize efficiently over a variety of objectives, which parameterize the reward function. We demonstrate that by altering the objectives passed as input to the policy, users gain the freedom to adjust its behavior or re-balance optimization targets at runtime, without need for collecting additional observation batches or re-training.

Simon Eisenmann, Daniel Hein, Steffen Udluft et al.

This paper presents the first algorithm for model-based offline quantum reinforcement learning and demonstrates its functionality on the cart-pole benchmark. The model and the policy to be optimized are each implemented as variational quantum circuits. The model is trained by gradient descent to fit a pre-recorded data set. The policy is optimized with a gradient-free optimization scheme using the return estimate given by the model as the fitness function. This model-based approach allows, in principle, full realization on a quantum computer during the optimization phase and gives hope that a quantum advantage can be achieved as soon as sufficiently powerful quantum computers are available.

Daniel Hein, Simon Wiedemann, Markus Baumann et al.

Quantum policy evaluation (QPE) is a reinforcement learning (RL) algorithm which is quadratically more efficient than an analogous classical Monte Carlo estimation. It makes use of a direct quantum mechanical realization of a finite Markov decision process, in which the agent and the environment are modeled by unitary operators and exchange states, actions, and rewards in superposition. Previously, the quantum environment has been implemented and parametrized manually for an illustrative benchmark using a quantum simulator. In this paper, we demonstrate how these environment parameters can be learned from a batch of classical observational data through quantum machine learning (QML) on quantum hardware. The learned quantum environment is then applied in QPE to also compute policy evaluations on quantum hardware. Our experiments reveal that, despite challenges such as noise and short coherence times, the integration of QML and QPE shows promising potential for achieving quantum advantage in RL.

Philipp Wissmann, Daniel Hein, Steffen Udluft et al.

This paper investigates the instability of Q-learning in continuous environments, a challenge frequently encountered by practitioners. Traditionally, this instability is attributed to bootstrapping and regression model errors. Using a representative reinforcement learning benchmark, we systematically examine the effects of bootstrapping and model inaccuracies by incrementally eliminating these potential error sources. Our findings reveal that even in relatively simple benchmarks, the fundamental task of Q-learning - iteratively learning a Q-function from policy-specific target values - can be inherently ill-posed and prone to failure. These insights cast doubt on the reliability of Q-learning as a universal solution for reinforcement learning problems.

Phillip Swazinna, Steffen Udluft, Daniel Hein et al.

Offline reinforcement learning (RL) Algorithms are often designed with environments such as MuJoCo in mind, in which the planning horizon is extremely long and no noise exists. We compare model-free, model-based, as well as hybrid offline RL approaches on various industrial benchmark (IB) datasets to test the algorithms in settings closer to real world problems, including complex noise and partially observable states. We find that on the IB, hybrid approaches face severe difficulties and that simpler algorithms, such as rollout based algorithms or model-free algorithms with simpler regularizers perform best on the datasets.