Multi-agent learning in stochastic N-player games is a notoriously difficult problem1 because, in addition to their changing strategic decisions, the players of the game2 must also contend with the fact that the game itself evolves over time, possibly in a3 very complicated manner. Because of this, the equilibrium convergence properties4 of popular learning algorithms - like policy gradient and its variants - are poorly5 understood, except in specific classes of games (such as potential or two-player,6 zero-sum games). In view of all this, we examine the long-run behavior of policy7 gradient methods with respect to Nash equilibrium policies that are second-order8 stationary (SOS) in a sense similar to the type of KKT sufficiency conditions9 used in optimization. Our analysis shows that SOS policies are locally attracting10 with high probability, and we show that policy gradient trajectories with gradient11 estimates provided by the Reinforcealgorithm achieve an O(1/ n) convergence12 rate to such equilibria if the method's step-size is chosen appropriately.

Recent years have seen embodied visual navigation advance in two distinct directions: (i) in equipping the AI agent to follow natural language instructions, and (ii) in making the navigable world multimodal, e.g., audio-visual navigation. However, the real world is not only multimodal, but also often complex, and thus in spite of these advances, agents still need to understand the uncertainty in their actions and seek instructions to navigate.

Multi-Agent Reinforcement Learning (MARL) has demonstrated significant success by virtue of collaboration across agents. Recent work, on the other hand, introduces surprise which quantifies the degree of change in an agent's environment. Surprise-based learning has received significant attention in the case of single-agent entropic settings but remains an open problem for fast-paced dynamics in multi-agent scenarios. A potential alternative to address surprise may be realized through the lens of free-energy minimization. We explore surprise minimization in multi-agent learning by utilizing the free energy across all agents in a multi-agent system. A temporal Energy-Based Model (EBM) represents an estimate of surprise which is minimized over the joint agent distribution. Our formulation of the EBM is theoretically akin to the minimum conjugate entropy objective and highlights suitable convergence towards minimum surprising states.