We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. Following recent research trends, we rely on the fundamental yet interpretable models of deterministic finite automata (DFAs) and linear temporal logic (LTL_f) formulas. In contrast to most existing works for learning DFAs and LTL_f formulas, we consider learning from only positive examples. Our motivation is that negative examples are generally difficult to observe, in particular, from black-box systems. To learn meaningful models from positive examples only, we design algorithms that rely on conciseness and language minimality of models as regularizers. Our learning algorithms are based on two approaches: a symbolic and a counterexample-guided one. The symbolic approach exploits an efficient encoding of language minimality as a constraint satisfaction problem, whereas the counterexample-guided one relies on generating suitable negative examples to guide the learning. Both approaches provide us with effective algorithms with minimality guarantees on the learned models. To assess the effectiveness of our algorithms, we evaluate them on a few practical case studies.

We investigate multi-agent reinforcement learning for stochastic games with complex tasks, where the reward functions are non-Markovian. We utilize reward machines to incorporate high-level knowledge of complex tasks. We develop an algorithm called Q-learning with reward machines for stochastic games (QRM-SG), to learn the best-response strategy at Nash equilibrium for each agent. In QRM-SG, we define the Q-function at a Nash equilibrium in augmented state space. The augmented state space integrates the state of the stochastic game and the state of reward machines. Each agent learns the Q-functions of all agents in the system. We prove that Q-functions learned in QRM-SG converge to the Q-functions at a Nash equilibrium if the stage game at each time step during learning has a global optimum point or a saddle point, and the agents update Q-functions based on the best-response strategy at this point. We use the Lemke-Howson method to derive the best-response strategy given current Q-functions. The three case studies show that QRM-SG can learn the best-response strategies effectively. QRM-SG learns the best-response strategies after around 7500 episodes in Case Study I, 1000 episodes in Case Study II, and 1500 episodes in Case Study III, while baseline methods such as Nash Q-learning and MADDPG fail to converge to the Nash equilibrium in all three case studies.

We study a class of reinforcement learning tasks in which the agent receives its reward for complex, temporally-extended behaviors sparsely. For such tasks, the problem is how to augment the state-space so as to make the reward function Markovian in an efficient way. While some existing solutions assume that the reward function is explicitly provided to the learning algorithm (e.g., in the form of a reward machine), the others learn the reward function from the interactions with the environment, assuming no prior knowledge provided by the user. In this paper, we generalize both approaches and enable the user to give advice to the agent, representing the user’s best knowledge about the reward function, potentially fragmented, partial, or even incorrect. We formalize advice as a set of DFAs and present a reinforcement learning algorithm that takes advantage of such advice, with optimal con- vergence guarantee. The experiments show that using well- chosen advice can reduce the number of training steps needed for convergence to optimal policy, and can decrease the computation time to learn the reward function by up to two orders of magnitude.