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In many real world applications, reinforcement learning agents have to optimize multiple objectives while following certain rules or satisfying a list of constraints. Classical methods based on reward shaping, i.e. a weighted combination of different objectives in the reward signal, or Lagrangian methods, including constraints in the loss function, have no guarantees that the agent satisfies the constraints at all points in time and can lead to undesired behavior. When a discrete policy is extracted from an action-value function, safe actions can be ensured by restricting the action space at maximization, but can lead to sub-optimal solutions among feasible alternatives. In this work, we propose Constrained Q-learning, a novel off-policy reinforcement learning framework restricting the action space directly in the Q-update to learn the optimal Q-function for the induced constrained MDP and the corresponding safe policy. In addition to single-step constraints referring only to the next action, we introduce a formulation for approximate multi-step constraints under the current target policy based on truncated value-functions. We analyze the advantages of Constrained Q-learning in the tabular case and compare Constrained DQN to reward shaping and Lagrangian methods in the application of high-level decision making in autonomous driving, considering constraints for safety, keeping right and comfort. We train our agent in the open-source simulator SUMO and on the real HighD data set.

In the past few years, off-policy reinforcement learning methods have shown promising results in their application for robot control. Deep Q-learning, however, still suffers from poor data-efficiency and is susceptible to stochasticity in the environment or reward functions which is limiting with regard to real-world applications. We alleviate these problems by proposing two novel off-policy Temporal-Difference formulations: (1) Truncated Q-functions which represent the return for the first n steps of a target-policy rollout w.r.t. the full action-value and (2) Shifted Q-functions, acting as the farsighted return after this truncated rollout. This decomposition allows us to optimize both parts with their individual learning rates, achieving significant learning speedup. We prove that the combination of these short- and long-term predictions is a representation of the full return, leading to the Composite Q-learning algorithm. We show the efficacy of Composite Q-learning in the tabular case and compare Deep Composite Q-learning with TD3 and TD3(Delta), which we introduce as an off-policy variant of TD(Delta). Moreover, we show that Composite TD3 outperforms TD3 as well as state-of-the-art compositional Q-learning approaches significantly in terms of data-efficiency in multiple simulated robot tasks and that Composite Q-learning is robust to stochastic environments and reward functions.