Risk-Sensitive Multi-Agent Reinforcement Learning in Network Aggregative Markov Games

Classical multi-agent reinforcement learning (MARL) assumes risk neutrality and complete objectivity for agents. However, in settings where agents need to consider or model human economic or social preferences, a notion of risk must be incorporated into the RL optimization problem. This will be of greater importance in MARL where other human or non-human agents are involved, possibly with their own risk-sensitive policies. In this work, we consider risk-sensitive and non-cooperative MARL with cumulative prospect theory (CPT), a non-convex risk measure and a generalization of coherent measures of risk. CPT is capable of explaining loss aversion in humans and their tendency to overestimate/underestimate small/large probabilities. We propose a distributed sampling-based actor-critic (AC) algorithm with CPT risk for network aggregative Markov games (NAMGs), which we call Distributed Nested CPT-AC. Under a set of assumptions, we prove the convergence of the algorithm to a subjective notion of Markov perfect Nash equilibrium in NAMGs. The experimental results show that subjective CPT policies obtained by our algorithm can be different from the risk-neutral ones, and agents with a higher loss aversion are more inclined to socially isolate themselves in an NAMG.

Continuous Reinforcement Learning-based Dynamic Difficulty Adjustment in a Visual Working Memory Game

Dynamic Difficulty Adjustment (DDA) is a viable approach to enhance a player's experience in video games. Recently, Reinforcement Learning (RL) methods have been employed for DDA in non-competitive games; nevertheless, they rely solely on discrete state-action space with a small search space. In this paper, we propose a continuous RL-based DDA methodology for a visual working memory (VWM) game to handle the complex search space for the difficulty of memorization. The proposed RL-based DDA tailors game difficulty based on the player's score and game difficulty in the last trial. We defined a continuous metric for the difficulty of memorization. Then, we consider the task difficulty and the vector of difficulty-score as the RL's action and state, respectively. We evaluated the proposed method through a within-subject experiment involving 52 subjects. The proposed approach was compared with two rule-based difficulty adjustment methods in terms of player's score and game experience measured by a questionnaire. The proposed RL-based approach resulted in a significantly better game experience in terms of competence, tension, and negative and positive affect. Players also achieved higher scores and win rates. Furthermore, the proposed RL-based DDA led to a significantly less decline in the score in a 20-trial session.