Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players' actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players' reward parameters from observed state-action trajectories via a projected gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outperform those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.

Multi-Objective Controller Synthesis with Uncertain Human Preferences

Multi-objective controller synthesis concerns the problem of computing an optimal controller subject to multiple (possibly conflicting) objective properties. The relative importance of objectives is often specified by human decision-makers. However, there is inherent uncertainty in human preferences (e.g., due to different preference elicitation methods). In this paper, we formalize the notion of uncertain human preferences and present a novel approach that accounts for uncertain human preferences in the multi-objective controller synthesis for Markov decision processes (MDPs). Our approach is based on mixed-integer linear programming (MILP) and synthesizes a sound, optimally permissive multi-strategy with respect to a multi-objective property and an uncertain set of human preferences. Experimental results on a range of large case studies show that our MILP-based approach is feasible and scalable to synthesize sound, optimally permissive multi-strategies with varying MDP model sizes and uncertainty levels of human preferences. Evaluation via an online user study also demonstrates the quality and benefits of synthesized (multi-)strategies.

Towards Personalized Explanation of Robotic Planning via User Feedback

Prior studies have found that providing explanations about robots' decisions and actions help to improve system transparency, increase human users' trust of robots, and enable effective human-robot collaboration. Different users have various preferences about what should be included in explanations. However, little research has been conducted for the generation of personalized explanations. In this paper, we present a system for generating personalized explanations of robotic planning via user feedback. We consider robotic planning using Markov decision processes (MDPs) and develop an algorithm to automatically generate a personalized explanation of an optimal robotic plan (i.e., an optimal MDP policy) based on the user preference regarding four elements (i.e., objective, locality, specificity, and abstraction). In addition, we design the system to interact with users via answering users' further questions about the generated explanations. Users have the option to update their preferences to view different explanations. The system is capable of detecting and resolving any preference conflict via user interaction. Our user study results show that the generated personalized explanations improve user satisfaction, while the majority of users liked the system's capabilities of question-answering, and conflict detection and resolution.

Towards Transparent Robotic Planning via Contrastive Explanations

Providing explanations of chosen robotic actions can help to increase the transparency of robotic planning and improve users' trust. Social sciences suggest that the best explanations are contrastive, explaining not just why one action is taken, but why one action is taken instead of another. We formalize the notion of contrastive explanations for robotic planning policies based on Markov decision processes, drawing on insights from the social sciences. We present methods for the automated generation of contrastive explanations with three key factors: selectiveness, constrictiveness, and responsibility. The results of a user study with 100 participants on the Amazon Mechanical Turk platform show that our generated contrastive explanations can help to increase users' understanding and trust of robotic planning policies while reducing users' cognitive burden.