Risk-sensitive Multi-agent Reinforcement Learning In Network Aggregative Markov Games

Abstract

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

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