SocialJax: An Evaluation Suite for Multi-agent Reinforcement Learning in Sequential Social Dilemmas

Social dilemmas pose a significant challenge in the field of multi-agent reinforcement learning (MARL). Melting Pot is an extensive framework designed to evaluate social dilemma environments, providing an evaluation protocol that measures generalization to new social partners across various test scenarios. However, running reinforcement learning algorithms in the official Melting Pot environments demands substantial computational resources. In this paper, we introduce SocialJax, a suite of sequential social dilemma environments implemented in JAX. JAX is a high-performance numerical computing library for Python that enables significant improvements in the operational efficiency of SocialJax on GPUs and TPUs. Our experiments demonstrate that the training pipeline of SocialJax achieves a 50\texttimes{} speedup in real-time performance compared to Melting Pot's RLlib baselines. Additionally, we validate the effectiveness of baseline algorithms within the SocialJax environments. Finally, we use Schelling diagrams to verify the social dilemma properties of these environments, ensuring they accurately capture the dynamics of social dilemmas.

Learning the Expected Core of Strictly Convex Stochastic Cooperative Games

Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in credit assignment is the core, which is the set of stable allocations where no agent has the motivation to deviate from the grand coalition. In this paper, we consider the stable allocation learning problem of stochastic cooperative games, where the reward function is characterised as a random variable with an unknown distribution. Given an oracle that returns a stochastic reward for an enquired coalition each round, our goal is to learn the expected core, that is, the set of allocations that are stable in expectation. Within the class of strictly convex games, we present an algorithm named \texttt{Common-Points-Picking} that returns a stable allocation given a polynomial number of samples, with high probability. The analysis of our algorithm involves the development of several new results in convex geometry, including an extension of the separation hyperplane theorem for multiple convex sets, and may be of independent interest.

Double Thompson Sampling in Finite stochastic Games

We consider the trade-off problem between exploration and exploitation under finite discounted Markov Decision Process, where the state transition matrix of the underlying environment stays unknown. We propose a double Thompson sampling reinforcement learning algorithm(DTS) to solve this kind of problem. This algorithm achieves a total regret bound of $\tilde{\mathcal{O}}(D\sqrt{SAT})$in time horizon $T$ with $S$ states, $A$ actions and diameter $D$. DTS consists of two parts, the first part is the traditional part where we apply the posterior sampling method on transition matrix based on prior distribution. In the second part, we employ a count-based posterior update method to balance between the local optimal action and the long-term optimal action in order to find the global optimal game value. We established a regret bound of $\tilde{\mathcal{O}}(\sqrt{T}/S^{2})$. Which is by far the best regret bound for finite discounted Markov Decision Process to our knowledge. Numerical results proves the efficiency and superiority of our approach.