Reinforcing the World's Edge: A Continual Learning Problem in the Multi-Agent-World Boundary

Abstract: Reusable decision structure survives across episodes in reinforcement learning, but this depends on how the agent--world boundary is drawn. In stationary, finite-horizon MDPs, an invariant core: the (not-necessarily contiguous) subsequences of state--action pairs shared by all successful trajectories (optionally under a simple abstraction) can be constructed. Under mild goal-conditioned assumptions, it's existence can be proven and explained by how the core captures prototypes that transfer across episodes. When the same task is embedded in a decentralized Markov game and the peer agent is folded into the world, each peer-policy update induces a new MDP; the per-episode invariant core can shrink or vanish, even with small changes to the induced world dynamics, sometimes leaving only the individual task core or just nothing. This policy-induced non-stationarity can be quantified with a variation budget over the induced kernels and rewards, linking boundary drift to loss of invariants. The view that a continual RL problem arises from instability of the agent--world boundary (rather than exogenous task switches) in decentralized MARL suggests future work on preserving, predicting, or otherwise managing boundary drift.