Discovering Learning Rules that Shape Others

A key milestone toward Recursive Self-Improvement (RSI) is replacing hand-crafted optimizers with meta-learned update rules (such as Disco103 and OPEN) that discover how agents learn. Yet when a self-discovered RL model trains with adapting teammates, does co-evolution sustain capability gains or trap agents in brittle conventions? Across 1,800+ runs in continuous collective robotics (VMAS) and discrete coordination (Overcooked), we establish five laws of multi-agent adaptation. First, four-cell counterfactual partner swaps expose an evaluation illusion: apparent team progress often masks focal regression (+1.066 team gain concealing -0.119 focal loss) and inflates transfer by +0.649 to +1.210. Second, a 288-run physical-coupling sweep ($α\in [0, 1.5]$) reveals a linear scaling law ($β= +0.255$, $p = 0.000488$, Spearman $ρ= 1.0$): live reciprocal feedback keeps Disco103 invariant (AUC 0.297--0.322), whereas severing feedback triggers a monotonic collapse (-0.172 to -0.490), with OPEN establishing a sensitivity spectrum (Disco103 > OPEN > MAPPO). Third, extending navigation training eightfold (1.05M steps) enables Disco103 to overtake MAPPO (+0.087 team return, +0.133 bank gain), while decoupled training boosts cross-partner completion by +10.16% (56.25% vs. 46.09%). Fourth, in Overcooked, MAPPO's self-play conventions induce a 28.13% cross-partner collision rate, whereas Disco103 cuts collisions to 12.77% and achieves 3.33x higher bank return (9.96 vs. 2.99; net gain +6.43), further improved by decoupled meta-adaptation (+1.39 with scripted partners). Finally, perturbation pulses ($p=0.00098$), auxiliary entropy diagnostics (8.485 nats), and 48 multi-lifetime meta-evolved rules ($L_2 \in [2.11, 4.91]$) trace these dynamics to partner-gradient blindness and auxiliary drift, informing multi-agent self-discoverd algorithms.

Human coordination often relies on the ability to influence the beliefs of others through strategic action. In multi-agent reinforcement learning, opponent shaping attempts to replicate this influence, though existing methods typically operate within an opponent's parameter, policy, or value space. Meanwhile, belief-manipulation techniques in hidden-role games often rely on hard-coded objectives, such as deception or belief saturation. We propose Differentiable Belief-based Opponent Shaping (D-BOS), a first-order method that treats each observer's belief as the shaped opponent state and differentiates through $k$-step softmax-Bayes belief dynamics. Rather than explicitly rewarding deceptive or cooperative behavior, our method treats the belief state as the target for shaping. This allows the optimal strategy to emerge naturally from the environment's reward structure. This belief-space formulation provides an opponent-shaping signal by differentiating through opponent belief updates, and naturally extends to multiple observers by aggregating gradients over their individual inferred belief trajectories. Empirically, D-BOS outperforms PPO and BBM in hidden-role games, with the largest gains in mixed-motive settings.

Deep reinforcement learning agents in partially observable competitive games must act on beliefs about an unseen opponent's intent. We study a spatial opponent model: a transformer trained with hindsight-relabelled opponent goals that outputs a subgoal heatmap from the opponent's observed trajectory, fused early into a dueling double DQN. In symmetric constant-sum foraging games with partial observability, the module stabilises training. Plain TD(0) DQN suffers degenerate seeds in three of four one-step configurations, whereas the opponent-model agent never collapses and, wherever training succeeds, recovers the majority of the symmetric game value. Transfers zero-shot to a foraging opponent unseen by the learner, with a positive goal advantage over the baseline, and loses this edge exactly where an information argument predicts: against a full-information tracking adversary whose intent is the learner itself, and on resource-dense maps where both agents saturate. A blindfold ablation, zeroing the heatmap at deployment, decomposes the advantage into two mechanisms: training-time stabilisation, which dominates where the credit assignment is hard and survives blinding on the dense map, and deployment-time inference, whose reliance shrinks as fog thins on the sparse map. We conclude that opponent-goal inference is a stability-and-transfer mechanism whose value is governed by measurable boundary conditions: visibility (fog thickness), opponent intent, and resource density.