Negotiated Reasoning: On Provably Addressing Relative Over-Generalization

Over-generalization is a thorny issue in cognitive science, where people may become overly cautious due to past experiences. Agents in multi-agent reinforcement learning (MARL) also have been found to suffer relative over-generalization (RO) as people do and stuck to sub-optimal cooperation. Recent methods have shown that assigning reasoning ability to agents can mitigate RO algorithmically and empirically, but there has been a lack of theoretical understanding of RO, let alone designing provably RO-free methods. This paper first proves that RO can be avoided when the MARL method satisfies a consistent reasoning requirement under certain conditions. Then we introduce a novel reasoning framework, called negotiated reasoning, that first builds the connection between reasoning and RO with theoretical justifications. After that, we propose an instantiated algorithm, Stein variational negotiated reasoning (SVNR), which uses Stein variational gradient descent to derive a negotiation policy that provably avoids RO in MARL under maximum entropy policy iteration. The method is further parameterized with neural networks for amortized learning, making computation efficient. Numerical experiments on many RO-challenged environments demonstrate the superiority and efficiency of SVNR compared to state-of-the-art methods in addressing RO.